The management of socioeconomic safety 9781443891196, 1443891193

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The Management of Socioeconomic Safety

The Management of Socioeconomic Safety By

Eugene Solozhentsev

The Management of Socioeconomic Safety By Eugene Solozhentsev This book first published 2017 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2017 by Eugene Solozhentsev All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-9119-3 ISBN (13): 978-1-4438-9119-6

CONTENTS

Abbreviations .............................................................................................. x Abstract ...................................................................................................... xi Foreword ................................................................................................... xii Introduction ............................................................................................... xv Chapter One ................................................................................................. 1 Scientific Foundations of Top-economics 1.1. Components of Top-economics ...................................................... 1 1.2. Definitions of Invalidity .................................................................. 3 1.3. Advantages and Features of Top-economics .................................. 5 1.4. Boolean Events-propositions in Economic Safety .......................... 6 1.5. New Types of LP-risk Models ..................................................... 10 1.5.1. Hybrid LP-risk Model of Risk of Failure to Solve Difficult Problems ...................................................... 11 1.5.2. LP-models of Invalidity of Socioeconomic Systems............ 14 1.5.3. Conceptual LP-risk Models of Forecasting Invalidity.......... 14 1.5.4. Indicative LP-risk Models of the System’s Danger State ..... 17 1.6. Database and Knowledge Base of Socioeconomic Systems ......... 20 1.6.1. Data Structure and Statistical Database ................................ 21 1.6.2. Events-parameters and Events-grades ................................. 22 1.6.3. The Transition from the Database to the Knowledge Base .. 23 1.6.4. The Knowledge Base and the System of L-equations .......... 24 1.7. Incompatible Events Groups ......................................................... 25 1.7.1. Logic and Probabilities in Incompatible Events Groups ...... 25 1.7.2. The Bayes Formula for Probabilities in Incompatible Events Groups................................................. 28 1.8. Risk Management Technologies in Structure-complex Systems (SCS) ............................................ 28 1.8.1. Components of Risk Management Technologies ................ 29 1.8.2. Classes of LP-risk Models ................................................... 30 1.8.3. Risk Management Technologies Procedures ....................... 33 1.8.4. Research Topics on Risk Management Technologies ......... 35

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1.9. Development of LP-risk Models of Socioeconomic Systems ...... 37 1.9.1. Formal Methods of Development ........................................ 37 1.9.2. Associative LP-risk Models ................................................ 39 1.9.3. Tabular Assignment of LP-risk Models .............................. 40 1.9.4. Development of Complex LP-risk Models .......................... 42 1.9.5. Development of Invalidity LP-models of Systems .............. 43 1.10. Risk LP-analysis of Socioeconomic System States .................... 44 1.11. LP-forecasting of Risk in States Space ....................................... 46 1.12. Risk LP-management of Socioeconomic Systems ...................... 48 1.13. Dynamism of LP-risk Models .................................................... 49 1.14. Synthesis of Events Probabilities ............................................... 50 1.15. Regulation and Management in Economics ................................ 52 1.16. Objective and Subjective Invalidity ............................................ 53 1.17. Connection between SES and Environment................................ 53 1.18. Unforgotten Knowledge.............................................................. 54 1.19. Concepts and Principles of Safety Management of SES ............. 56 Chapter Two .............................................................................................. 58 Examples of Logical and Probabilistic Management of Economic Safety 2.1. Logical and Probabilistic Risk Management of Economic State of Russia ......................................................... 59 2.1.1. LP-risk Model of Economic State ........................................ 59 2.1.2. LP-risk Analysis of Economic State..................................... 66 2.1.3. LP-risk Management of Economic State .............................. 67 2.1.4. LP-management of Economic War with Sanctions .............. 67 2.1.5. LP-risk Management of Economic Evolution of Country .... 68 2.1.6. Improvement and Correction of LP-risk Model ................... 69 2.2. LP-management of the Country’s Innovation System .................. 70 2.2.1. Global Innovative Index ....................................................... 71 2.2.2. Logic Global Innovative Index ............................................. 74 2.2.3. Analysis of the Development and Evaluation of Innovation of RMT SCS....................................................... 81 2.2.4. Hybrid LP-model of Failure of Solution of Innovation Problem .............................................................. 88 2.2.5. Indicative LP-model of State Danger of Innovation System ................................................................ 91 2.3. LP-models for Counteraction against Corruption ........................ 93 2.3.1. Axioms for Counteraction against Bribery and Corruption.. 94 2.3.2. Hybrid LP-model of Failure in Counteracting Corruption .. 95 2.3.3. LP-model to Counter Bribery in an Institution ..................... 97

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2.3.4. LP-model to Counter Bribery in the Behavior of Officials ................................................................................ 99 2.3.5. LP-model to Counter Bribery based on Analysis of Service Parameters ............................................................. 104 2.3.6 Conclusions ......................................................................... 105 2.4. LP-models for Countering Drug Addiction ................................ 106 2.4.1. Selecting the Models Type ................................................. 106 2.4.2. LP-models of Failure in Counteracting Drug Addiction .... 108 2.4.3. The Conceptual LP-risk Model of Forecasting Drug Addiction in a Region .................................................... 111 2.4.4. The Fundamental Characteristics of the Drug Situation in the Region........................................................................... 115 2.4.5. The Indicative LP-model of Danger of the Drug Situation .............................................................. 120 2.4.6. Calculations ........................................................................ 126 2.4.7 Conclusion........................................................................... 127 2.5. LP-models of Operational Risk and Reserve of Capital under Basel .................................................................. 128 2.5.1. Logical and Probabilistic Models of Operational Risk of a Bank ................................................ 130 2.5.2. Calculation of Capital to Cover .......................................... 133 2.5.3. Integration of Models ......................................................... 134 2.6. Invalidity LP-model for Quality Management of Systems and Products under WTO ............................................................. 140 2.6.1. Construction of LP-model of System Invalidity ................. 140 2.6.2. Description of Invalid Events ............................................. 143 2.7. LP-models, Monitoring and Management of the Crediting Process in Banks ................................................ 144 2.7.1. Statement of the Problem ................................................... 144 2.7.2. The LP-model of Credit Risk ............................................. 145 2.7.3. Identification of LP-models of Credit Risk ........................ 146 2.7.4. LP-analysis of Credit Risk ................................................. 150 2.7.5. Inability to Create the Testing Samples .............................. 151 2.7.6. Monitoring Technology ...................................................... 153 2.7.7. Replacement of Risk Models.............................................. 157 2.7.8. Management of Crediting Process...................................... 160 2.8. LP-management of Risk and Efficiency of the Restaurant “Prestige” ......................................................... 162 2.8.1. Initiating Parameters and their Graduations ....................... 163 2.8.2. Database and Knowledge Base about States of the Restaurant ..................................................................... 164

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2.8.3. Frequency Analysis of Risk and Efficiency ....................... 167 2.8.4. LP-analysis of Risk and the Efficiency of the Restaurant .. 170 2.8.5. Risk Analysis by Contributions of Parameters ................... 174 2.9. LP-models of Failure of Management of ZAO “Transas” .......... 175 2.9.1. State of the Problem ........................................................... 176 2.9.2. Characteristics of the Company.......................................... 176 2.9.3. Failure of Management by Functions ................................. 177 2.9.4. Failure of Management by Business Direction .................. 178 2.9.5. Failure of Management in Achieving of Objectives Groups .............................................................. 179 2.9.6. Management of Quality Functioning of the Company ....... 181 Chapter Three .......................................................................................... 186 Special Software for Problems of Economic Safety 3.1. Software “Arbiter” for the Modeling of Structure-logic............. 186 3.2. Software “ROCS 2” for Analysis of Risk of Big Systems ........ 188 3.3. Software “Cortege Algebra” for Arbitrary Logic Functions....... 190 3.4. Software for the Class “LP-classification”................................. 192 3.5. Software for the Class “LP-efficiency”....................................... 194 3.6. Software for the Synthesis of Events Probabilities ..................... 195 3.7. The Scheme of Modeling and Analysis of Risk in the Big System ......................................................................... 200 3.8. What Maths is needed for Economics? ...................................... 201 3.9. Sets of Software for Different Classes of LP-risk Models ......... 202 Chapter Four ............................................................................................ 204 State of the Problem of Management of Economic Safety 4.1. Relevance of the Problem of Management of Economic Safety ...................................................................... 204 4.2. Fundamentals of the Problem of Economic Safety Management ...................................................................... 206 4.3. Realization of the Problem of Economic Safety Management ... 207 4.4. Perspectives of Management Problem of Economic Safety ....... 210 4.5. The need for Reform of Education, Science and Economy ........ 212 4.6. The need to Improve Construction Strategies for the Socioeconomic Evolution of Regions .............................. 213 4.7. Subject Index of the Discipline “Socioeconomic Safety Management” ......................................... 215

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Conclusion ............................................................................................... 217 References ............................................................................................... 220 Subject Index ........................................................................................... 227

ABBREVIATIONS

IE – initiating events LP – logical and probabilistic (model) SES – socioeconomic systems SES-1 – of paramount importance SES for the State, designed to reduce the loss of funds and increase their income SES-2 – complex SES for the State and regions, depending on the number of ministries and departments SES-3 – local SES for companies and firms, the success of which depends largely on their desires and capabilities SSM — socioeconomic safety management RMT SCS — risk management technologies of structurally complex systems Top-economics — management of economic safety of SES WTO — World Trade Organisation

ABSTRACT

The book introduces a new academic discipline “Socioeconomic safety management” (SSM) on the basis of logical and probabilistic (LP) risk models. The definitions of invalidity in economics by analogy with reliability in engineering are given. The special features and advantages of the SSM discipline and its components are described: methods, models, technologies, tasks, objects and special software. New types of Boolean “events-propositions” in economics are introduced, as well as the new types of LP-risk models. SSM has the following research objects — socioeconomic systems SES-1, which are of top priority for the country and are aimed at reducing financial losses and increasing revenues; SES-2 which are complex ones, depending on several ministries and government agencies; SES-3, which are local ones, for companies and firms. The tasks of SSM are discussed: the construction of LP-risk models, LP-analysis, LP-forecasting and LPmanagement of SES state risk. The applications of SSM for SES include: the management system for innovations, corruption counteraction, drug addiction counteraction, assessment of banks’ operating risk and capital reservation in accordance with Basel, management of systems and goods quality by WTO, bank loans management. Within the framework of economic safety the problems of risk modeling, analysis and management are solved, as well as the management of economic wars by the use of sanctions. Our examples have demonstrated that: 1) it is very difficult to solve socioeconomic problems without the involvement of scientists and public opinion, 2) the creation of top priority SES is impossible without reforms in education, science and economy, 3) the future development of the SSM requires the certification of special software. The book is intended for economists and managers who are interested in the problem of SES economic safety management. It will be also useful to undergraduate and postgraduate students of economics and their teachers.

FOREWORD

Economics is far from being perfect and needs to be developed further. This can be seen from the failures of companies, economic recessions in many countries and unsolved problems in economics. Let us name just a few problems in economics, unsolved due to the lack of or incorrectness of the following mathematical models of system states: connections between economy, politics, State, science and society; taking into consideration events-statements made by government officials, businessmen, scientists and public figures concerning changes in legislation, the situation in the market, the emergence of innovations, etc.; the interconnection of different socioeconomic systems (SES); transition from any databases to knowledge bases in order to make decisions; using multi-state invalidity in economics in the same way as failures in engineering; the techniques of building system risk models using the parameters of one of its states; invalid, conceptual, indicative and hybrid models built for the universal assessment of economic systems; the integration of models by logical operations AND, OR, NOT; the study course “Socioeconomic safety management” for economic departments. Economics departments at universities (created on the basis of accounting and audit departments) and academic institutions under the name of “Economic safety” do not actually deal with safety management. Here are some more problems in economics which are unsolved due to the lack of or incorrectness of the following mathematical models of management: taking decisions using mainly certain “notions” and “manual operations”; management of the banks’ operating risk and capital reservation by Basel; management of the quality of systems and products by WTO; management of the crediting process in banks; management of economic wars caused by sanctions; management of reforms in education, science and economy; management of the participation of public opinion and scientists in the solution of socioeconomic problems; the development of systems as complex objects moving along a pre-set trajectory with corrections in case of deviations from it; management of the strategy of the development of a country and its regions on the basis of adjustments of models using information concerning the changes in economy, politics, law and innovations.

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The efficiency of LP-management is considered using the example of managing a country’s SES safety. Socio-economic safety management is being made more difficult because of the following factors: management has a complex character, as it depends on several ministries, institutions and legal authorities; we do not have a unified system of models, methods, tasks, techniques and special software for managing socioeconomic safety. Sets and LP-models, according to some scientists, are the simplest and most transparent aspects of mathematics. Socioeconomic safety should be managed on the basis of mathematical models and not by “notions”, which are often erroneous. The analysis of unsolved problems in economics has shown that we need a new economic discipline “Socio-economic safety management”. This new academic discipline has been influenced by many scientists: G. Boole who introduced the logical calculus of sentences; P. Poretsky who established the connection between logic and probability theory; I. Ryabinin who created the theory of LP-ɚnalysis of reliability in engineering; Nobel Prize winners J. Buchanan and J. Heckman who studied the interconnection of economy, politics and the State on the basis of games theory and statistical data analysis; N. Wiener and J. von Neumann who believed that mathematical methods, used for managing economic and social systems, must be based on logic, probability theory, sets and the combinatorial theory; Ⱥ. Einstein who thought that no problem could be solved at the level where it appeared. The book defines the invalidity of parameters and the system as a deviation from pre-set values. It introduces new types of Boolean eventspropositions and new types of logical probabilistic (LP) risk models for managing socio-economic safety. We use the event approach to modeling the risk of systems and solving the problems of risk analysis, forecasting and management. We should consecutively build scenario, structural, logical and probabilistic risk models for a socio-economic system. In the SES safety management technique the central place is occupied by the following procedures: the orthogonalization of the risk logical function, the assessment of the invalidity of initiating events and the LP-analysis of system risk by the contributions of events. The new economic discipline “Socioeconomic safety management” is a unified complex of models, methods, knowledge, techniques and software based on LP-risk models and LP-calculus. The academic and practical relevance of this discipline is defined by the fact that it solves the unsolved problems in economics mentioned above.

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Foreword

The efficiency of an economy will increase if, together with the tasks of microeconomics and macroeconomics, we solve the tasks of socioeconomic safety management. The book introduces new scientific directions: “Management of socioeconomic safety” and “The top level of managing in economics”. The objects of management include: governments, socioeconomic problems of governments, socioeconomic systems of a country and its regions. The author Honoured scientist of the Russian Federation, Doctor of Technical Sciences, Professor, Saint-Petersburg State University of Aerospace Instrumentation, Faculty of Economics.

INTRODUCTION

Economic efficiency can increase if together with the tasks of micro- and macroeconomics we deal with the problems of top-economics or economic safety management. E. Solozhentsev

The academic discipline “Reliability and Safety” exists in engineering, but not in economics, though failures, recessions, crises and bankruptcies are very common in an economy. We call the academic discipline “economic reliability” or “socioeconomic safety management”. The problem of socioeconomic safety management (SSM) of socioeconomic systems (SES) of a country, its regions, cities and companies has a high (top) mission, and for short we call it “topeconomics”, by analogy with the terms “microeconomics” and “macroeconomics”. Top-economics has its own methods, models, technologies, objects, tasks and software for the management of economic safety of SES. The safety of a country depends not only on its military, technological, energy, ecological and information safety [1], but also on its economic safety – sustainable development of its socioeconomic systems, and of the systems counteracting corruption, the systems counteracting drug addiction, etc. A lot of resources are required for the management of the State and evolution of socioeconomic systems. Therefore, a SES is needed for innovations management in order to reduce financial losses and increase revenues from industry and business. We have adopted as the basis the principle of a Chinese political leader Li Keqiang, according to which technological innovations are viewed as equal to innovations in management, including State management. A lot of departments of economics faculties, regional centers and research institutes bear a loud name “Economic safety”. The topics of their research and publications prove that they view economic safety management as guided by their own rules, which are very different and changeable, depending on who sets them. We propose universal rules of

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Introduction

economic safety management, based on logical probabilistic (LP) risk models. We formulate a risk scenario and build LP-risk models of failure risk of SES states, and we use monitoring data of indicators of SES and signaling events for changes in the economy, politics, laws and innovations, etc. to correct the probabilities of initiating events in the LPrisk model of SES. We carry out assessment, analysis and forecasting of SES risk and managing risk, making decisions about allocating resources to change the probabilities of initiating events. We develop the concept of management of the economic safety of a country, bringing together the management of the innovation system and SES economic safety. We present some examples of the management of SES economic safety based on LP-risk models and LP-calculus too. The author established the basic principles of building automated management systems by developing (debugging) structurally complex engineering systems (doctorate thesis, Institute of Cybernetics, Ukrainian Academy of Sciences, 1982). An engineering system (for example, a motor) consists of subsystems. There are certain initiating events (IE), which cause the destruction of subsystems and systems or their invalid performance (deviation from the norm). A table of the connections of the states (failures of subsystems) and initiating events is built. Common initiating events (parameters) define the connections of the states of subsystems. Using the connections table one builds LP-risk models of system state for assessment, analysis, forecasting and management by debugging (development). LP-risk models are also built for the management of the State and evolution of economic safety of SES (and a country). The success of a country (a complex system) is viewed as an event with a certain probability. Invalid events are considered. They denote the deviation of the state of an economic system from norms and requirements. Socioeconomic systems have common initiating events, which provide their interconnection. It is easy to combine logically the LP-risk models of different SES into one LP-risk model, which should be used to deal with the tasks of assessment, analysis, and forecasting of risk of the state and development of SES and the country. Economic safety management does not belong to top priority fundamental directions in science, defined by the Government of the Russian Federation and the Russian Academy of Sciences (RAS). The Russian Scientific Foundation also offers no grants for research in economic safety management. And this is not surprising, as certain

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Russian economists do not consider economics to be a fundamental science. The book deals with one of the sections of the new scientific direction in economic science. Content management of socioeconomic security is virtually non-existent. The author was guided mainly by the ideas of John Boole on the truth of propositional logic and Nobel Prize laureates James Buchanan [2] and James Heckman [3] on the interconnection of economics and politics in the development of the State on the basis of game theory and of statistical data analysis. Developing their ideas we offer a new approach to the analysis and economic safety management of SES, which is based on top-economics. The connections between economy, politics and society are considered in a broad aspect. The LP-risk model takes into account: x initiating events, which depend on the government’s decisions, the laws on education, science, social programmes, competition, legal protection of mothers and families, living standards, the level of medical care and other actions; x the ability of subjects (State, business and society) to solve the SES problems, depending on their desires and capabilities; x alarm events - changes in economy, politics, laws and legislation, innovation, natural disasters and wars, to change the situation on the world market for the correction of initiating events probability in the LP-risk model of SES. Objective – the creation of the scientific foundation for the economic safety of SES based on LP-risk models and the development of examples of the management of SES economic safety. This objective presupposes dealing with the following problems: 1. Introduction of a new academic discipline “top-economics” for the economic safety management of socioeconomic systems; 2. Definition of invalidity in economics by analogy with reliability in engineering; 3. Clarification of the features of a new academic discipline “topeconomics”; 4. Introduction of the new types of Boolean events-propositions and the new types of LP-risk models for economic safety management of SES; 5. Description of the components of top-economics: methods, models, technologies, tasks, objects and special software;

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6. Development of the techniques of logical probabilistic analysis, forecasting and risk management, as well as the technique of management of economic wars using sanctions; 7. Introduction of the technique of the synthesis of events probabilities in LP-risk models by non-numerical, incomplete and inaccurate expert information; 8. Development for top-economics of special software for structural logical simulation and synthesis of IE probabilities in LP-risk models; 9. Consideration of the examples of using top-economics for economic safety management of the country, its regions, cities, companies and their SES. Top-economics has the unified model system, methods, technologies, and software for managing the economic safety of SES with varying complexity. To indicate that this is a unified system of knowledge and methods, which are based on LP-models and LP-calculus, we propose the name “top-economics”. The discipline “top-economics” includes the following components: 1. Methods: the definitions of invalidity in economics and topeconomics; LP-calculus with “events-propositions”. 2. Models: hybrid LP-risk models of a problem’s solution failure, invalid LP-models of SES state, conceptual LP-models of development forecasting, indicative models of SES state danger. 3. Technologies of risk management in SES - structurally complex systems. 4. The tasks of assessment, analysis, forecasting and risk management. 5. Objects of management: SES of groups SES-1, SES-2, SES-3. 6. Special software. 7. Examples of management of SES economic safety. 8. Subject index. Invalidity LP-models can be applied in management of the state of socioeconomic systems under risk criteria. Also, these LP-models can be used for management of a system's development. Resources should be reserved for management of the state and development of systems. The following hierarchy of socioeconomic systems and problems can be established: large socioeconomic systems-countries, socioeconomic problems in countries, socioeconomic systems of the country (Russia).

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In the present work we consider in detail the tested LP-risk models for management of the safety of the socioeconomic system (SES) of a country (for example, Russia). These systems exist in reality and are understandable to everyone. With the use of LP-models the SES invalidity risk is estimated and analyzed. Resources and investments are allocated for invalidity management annually. Thus, the object of assessment, analysis and management is the following:Group SES-1, including the SES which are of top priority for the government, aimed at reducing financial losses and increasing revenues: 1. Management of the innovation’s system state of a country. 2. Counteraction to bribery and corruption. 3. Counteraction to drug addiction in a country. 4. Management of the banks’ risk and capital reservation in accordance with Basel. 5. Systems and goods quality management by WTO. 6. Monitoring and management of credit provision to banks. Group SES-2, containing complex SES for the State and the regions that depend on several ministries, agencies and legislative bodies: 1. The LP-risk model of a country’s birth rate. 2. The LP-model of the failure to solve the problem of education. ........................................................................................ 15. The LP-model of the failure to solve the problem of informatization. Group SES-3, containing local SES for companies and firms whose success depends mainly on their wishes and capabilities: 1. LP-management of risk and efficiency of the restaurant “Prestige”. 2. The LP-models of failure risk of managing ZAO “Transas”. .................................................................................... 25. The LP-risk models of the transportation company “Logwin Road + Rail Rus”. Note that micro- and macroeconomics do not solve the problem of the economic safety management of socioeconomic systems of groups SES-1, SES-2, SES-3 [4-6]. The following definitions of invalidity have been formulated for topeconomics:

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1. Invalidity in economics is introduced by analogy with reliability in technology. It has not two values (failure/non-failure), but a set of values to [0, 1]. 2. The international standard ISO 9000 – 2001 uses the term invalidity for assessing the quality of works, rendered services, products and management systems. 3. The invalidity of a system or a parameter is a deviation of their states from the states given by technical requirements and specifications. 4. An event-proposition corresponds to an invalid state. The degree of invalidity is considered as at risk. 5. This is the dialectic of subjective and objective in the assessment of invalidity: we set system requirements to the system subjectively and we consider objectively its status with respect to these requirements. 6. Constant parameters are not events in the system state. 7. The tasks of assessment, analysis, forecasting and risk management are solved by LP-models of SES invalidity risk. 8. LP-risk models of SES can be combined by logical operations AND, OR, NOT. Top-economics has the following features and advantages: 1. Target management of economic safety is carried out by the criterion of risk with the assessment of potential losses. 2. Top-economics has an interdisciplinary character, as it deals with economic, social, organizational, information and logical probabilistic aspects of the management of socioeconomic systems safety. 3. The system invalidity state is multi-state. 4. SES economic safety has a complex character, as it depends on several ministries, the government and legal bodies. 5. Connection of LP-risk models of the state of different SES can be realized via repeated initiating events (IE), which are part of LPrisk models of different SES. 6. The dynamics of LP-models of SES are provided by the correction of IE probabilities when new statistical data appear about system states, as well as new signal events concerning the changes in economy, politics, rights and laws, innovations, the situation in the world market, reforms in education, science and economy. 7. Construction of the LP-risk model using the parameters of one system state.

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8. Top-economics uses information and intellectual, innovative technologies of risk management in structurally complex systems. 9. Top-economics has transparent methods, models, techniques and tasks. The following new types of Boolean “events-propositions” appear in topeconomics: subjects’ failure events, signal events, invalidity events, conceptual events, indicative events, etc. In the economic safety management of SES instead of the probabilities of true/false events we use the probabilities of success/failure and hazardous/non-hazardous events. 1. Events-propositions about the non-success of subjects. An eventsubject is the failure by a subject to solve a difficult problem. The subjects are: the government, business, banks, academics, public opinion. 2. Signal events-propositions. We use only the fact of their occurrence in economics, politics, rules and laws, innovations, natural disasters and changes in the global market for the correction of probabilities of initiating events (IE) by non-numerical, inaccurate and incomplete expert information. 3. An event-proposition about invalidity is a proposition about the deviation of a parameter from zero or a given value. Parameters are normalized and have values within the range [0, 1]. An eventproposition about invalidity has the risk equal to the parameter value (the indicator). 4. Conceptual events-propositions predict the system’s evolution. The probabilities of the truth of events-propositions are evaluated by expert information. 5. Indicative events-propositions are considered as invalid events. Their measure of danger is the deviation of the parameter value from the given one. 6. Events-propositions about latency. The probabilities of eventspropositions are estimated by interviews and data from social networks. 7. Incompatible events in LP-risk models of SES are entered for grades of parameters. The following new types of LP-risk models with events-propositions are introduced in top-economics: 1. Hybrid LP-models of failure risk of solving difficult socioeconomic problems. They are built on the basis of risk scenarios for the

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subjects involved in solving the problem, and risk scenarios for objects-tasks that are at the heart of the problem; 2. Invalid LP-risk models. They are built on the basis of invalid events; 3. Conceptual LP-models of predicting the system’s evolution. They are built on the basis of the descriptions of the professionals who understand the nature of the problem; 4. Indicative LP-models of the system’s dangerous condition, built by indicative indicators which characterize the danger of the system’s state. All of these new types of LP-risk models can be used for each SES for the comprehensive analysis and management of its economic safety. The fundamental and novel character of top-economics is determined by the introduction of invalidity, the new types of Boolean eventspropositions and new types of LP-risk models, techniques, tasks, objects of management and special software. We can build the LP-models of a system’s success or failure. The probabilities of success and failure are linked by simple dependence: their sum equals 1. We shall use LP-risk models of failure in economic safety more often. Logical addition is used in these models (the risks are added), and then they are adjusted for system risk management. LP-risk models are developed in such a way as to ensure their monotony. This means that by increasing or decreasing the probability of any initiating event the probability (the risk) of the final event should increase or decrease correspondingly. The present work consists of the introduction, four chapters, conclusion, references and subject index. Chapter 1. “Scientific foundations of top-economics” gives the definitions of “invalidity” in economics by analogy with reliability in engineering. The features and advances of top-economics are described, after which we deal with the components of top-economics: its methods, models, technologies, tasks, objects and special software. The new types of Boolean events-propositions and new LP-risk models for economic safety management are introduced. Methods of building invalidity LPmodels are delineated. We offer the techniques of analysis, forecasting and management of risk of state and evaluation in LP-risk models. Further on we offer the technique of synthesis of the probabilities of events in LPmodels and take into account the dynamics in LP-risk models. The notions of objective and subjective senses in invalidity are considered.

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Chapter 2. “Examples of logical and probabilistic management of economic safety” focuses on the LP-risk model of the economic safety in Russia. The following LP-risk models are described: the state of the innovation system of the country, counteraction to bribery and corruption, counteraction to drug addiction, the management of the operation risk of a bank and capital reservation in accordance with Basel, the assessment of systems goods quality by WTO, monitoring and management of bank crediting. We also deal with the LP-models for managing the risk and efficiency of a restaurant, a transport company and the management of a company. Chapter 3. “Special software for problems of economic safety” considers the software for the class “LP-modeling”: “Arbiter” for the structural logic simulation, “ROCS 2” for analysis and optimization of the risk of large-scale systems, “Algebra of corteges” for arbitrary logic functions of risk. We also describe the software of classes “LPclassification” and “LP-efficiency” and software “Expa” for the synthesis of the probabilities of events in LP-risk models. We propose a set of software for the classes of risk models and bring out the algorithm of simulation and analysis of risk in a large system. We offer mathematical tools for economists: new Boolean events-propositions in economics, new LP-risk models with events-propositions, LP-calculus with eventspropositions; the identification method of nonlinear problems with many real valued variables and integer optimization criteria; the method of summary randomized indicators to assess the probabilities of events; the computational apparatus of cortege algebra for risk assessment of arbitrary systems of logic functions with many multi-states; the method of presenting logical variables in binary codes and actions with them in the LP-risk models of high dimension models; the proof of the impossibility of establishing equivalent training and testing samples in the classification of problems with LP-models. The question “what mathematical tools are required by economists for risk management?” is discussed. In Chapter 4 “State of the problem of management of economic safety” we justify the importance and the fundamental character of the economic safety management problem in Russia. In this chapter the reader will find various data from papers, books, special editions of journals in Russian and in English, from dissertations and State University of Aerospace Instrumentation (SUAI) students’ graduation and laboratory works, and from International Science Schools “Simulation and Analysis of Safety and Risk in Complex Systems”. The perspectives of topeconomics are closely linked with the creation of special inexpensive

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Introduction

software “Expa” and “Arbiter” for training the students of economics, as well as economists and company managers. In the Conclusion we give the expanded definition of top-economics as a system of models, methods, technologies and software for the management of the economic safety of SES of varying complexity. It is pointed out that top-economics considers the connection of economics, politics, business, science and society more broadly. We provide the general scheme of the management of economic safety of the country, the region and the company (system) based on top-economics. We illustrate the necessity of reforms in education, science and economy in the country. We also illustrate improved methods of developing strategies for the economic and social development of the regions. A conclusion is made that socioeconomic problems cannot be solved without the support of public opinion and scientists. The list of subject indexes of the scientific discipline “top-economics” is presented by the following sections: top-economics’ components, topeconomics’ features and the current evolutionary stage of top-economics. The author is also indebted to his former students Dr. V. Karasev, Dr. N. Lebedev, Dr. V. Alekseev, Dr. E. Karasev for their contributions in this volume. The author expresses special gratitude to Professors Eberhard Stickel (Germany), Hiromitsu Kumamoto (Japan) and Giovanni Barone-Adesi (Switzerland) for being given opportunities to visit their universities and for their teamwork in the field of risk. Sections 1.8 and 2.7 of the present book are written together with the candidate of technical sciences V. V. Karasev; sections 2.5 and 3.8 are written together with the candidate of economics E. I. Karaseva. The author is sincerely grateful to academician of RAS A.G. Aganbegyan for highlighting the key points in the book, to Doctor of Technical Sciences I. A. Ryabinin for his support and advice on logical probabilistic aspects, to Doctor of Mathematical and Physical Sciences V. P. Odinets and Doctor of Mathematical and Physical Sciences N. V. Hovanov for his valuable comments in reviewing the book. The book is addressed to managers and economists concerned with economic safety management of SES, undergraduate and graduate students and university professors of economics, as well as those from the branches of the Academy of Civil Service.

CHAPTER ONE SCIENTIFIC FOUNDATIONS OF TOP-ECONOMICS

No problem can be solved at the level where it appeared. Albert Einstein

In this chapter we establish the scientific foundations of top-economics and give the definitions of “invalidity” in economics by analogy with reliability in engineering, after which we pass on to describe the features and components of top-economics: its methods, models, technologies, tasks, objects and special software. We will consequently introduce the new types of Boolean “eventspropositions” and the new types of LP-risk models. The objects, analyzed and controlled by top-economics, are defined – three types of socioeconomic systems: SES-1 of top priority for the State; SES-2, which are complex ones for the State and the regions, depending on several ministries and government bodies; SES-3 – local ones for companies and firms. Analysis, forecasting and risk management procedures are considered. We will discuss the following problems: management and regulation in an economy, objectivity and subjectivity in invalidity, connection between SES and environment, unforgotten knowledge, and the concept and principles of SES safety management.

1.1. Components of Top-economics Top-economics has a unified system of models, methods, technologies, and software for the management of economic safety of SES with varying complexity. To define the unified system of knowledge and methods, which are based on LP-models and the LP-calculus, we propose the name “top-economics”. We propose to study and analyze economic safety management, applying universal rules, formulated for risk management technologies in structurally complex systems. The academic discipline “top-economics” or economic safety management in socioeconomic systems includes the following components [7, 8]:

2

Chapter One

1. Methods: The definitions (axioms) of invalidity in economics and top-economics, LP-calculus with Boolean “events-propositions”. 2. Models: Hybrid LP-risk models of the failure to manage complicated SES, invalid LP-risk models of SES states, the conceptual LP-model of SES development forecast, indicative LPmodels of SES state danger. 3. Risk management technologies in structurally complex systems. 4. The tasks of assessment, analysis, forecasting and risk management. 5. Special software. 6. Objects of management - socioeconomic systems of SES-1, SES2 and SES-3 groups. 7. Examples of economic safety management. 8. Subject Index. Top-economics deals with management objects belonging to three groups of SES. Group SES-1 consists of the SES which are of top priority for the State, aimed at reducing financial losses and increasing revenues: 1. The management of the state of the system of innovations of the country. 2. Counteraction to bribery and corruption. 3. Counteraction to drug addiction in the country. 4. Management of the operation risk of banks and capital reservation in accordance with Basel. 5. Management of the quality of systems and goods by WTO. 6. Monitoring and management of credit provision to banks. Group SES-2 contains complex SES for the State and regions, depending on several ministries and government bodies: 1. The LP-risk model of birth rate in the country. 2. The LP-risk model of death rate. 3. The LP-risk model of inflation growth. 4. The LP-risk model of economic growth slowing down. 5. The LP-risk model of decay in agriculture. 6. The LP-risk model of an environmental catastrophe. 7. The LP-risk model of actual salaries decrease. 8. The LP-risk model of unemployment rate growth. 9. The LP-risk model of educational system failure. 10. The LP-risk model of health care system failure. 11. The LP-risk model of the failure to solve the problem of a lack of kindergartens.

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12. The LP-model of the failure to solve the problem of building housing accommodation. 13. The LP-model of the failure to solve cultural problems. 14. The LP-model of the failure to solve the IT development problem. 15. The LP-model of the current situation with economic safety in Russia. Group SES-3 contains local SES for companies and firms, whose success mainly depends on their wishes and possibilities [7, 8]: 1. The LP-risk model of management and efficiency of a restaurant. 2. The LP-assessment of ratings and comparison of office centers in St. Petersburg. 3. The LP-risk model of the failure of a company ZAO BaltAvtoPoisk. 4. The LP-risk models of the failure of the management of ZAO Transas company. 5. The LP-risk model of a building company. 6. The LP-risk model of the transport company Logwin Road + RailRus. 7. The LP-model of the steel mill electrical supply safety. 8. The LP-model of the insurance of explosions and fires at hazardous objects. It should be noted that microeconomics and macroeconomics do not solve the problems of managing the economic safety of socioeconomic systems of groups SES-1, SES-2 and SES-3. There are up to 20 risk initiating indexes in the above mentioned SES, which is a lot fewer than the number of fundamental indexes describing SES states. The initiating events are connected with the derivative events by logical operations OR, AND. The examples of calculation research of economic safety management of several SES from groups SES-1, SES-2 and SES-3 are provided in Chapter 2.

1.2. Definitions of Invalidity The problem of a system’s invalidity has recently appeared. This problem accompanies technical progress and will be solved using economic tools and knowledge available in the considered period. The necessity of a special discipline concerning a system’s invalidity was caused by WTO requirements to estimate the system’s and the product’s quality, management of the state and development of socioeconomic

4

Chapter One

systems, estimation of risk of socioeconomic problem decision failure, forecast of system’s development, estimation of system’s state danger. Together with the usual sense of the word “invalidity”, which means the deviation of the system’s parameters from given values, for quantitative estimation of invalidity we need a more rigorous scientific definition of the term “invalidity”. Invalidity is an event which leads to a loss of a system’s quality, but a system can perform its assigned goals. The following definitions (axioms) are introduced for invalidity and top-economics: Definition 1. Invalidity in economics is introduced by analogy with reliability in engineering. Unlike reliability in engineering it has not two values (failure/non-failure), but a set of values in the interval [0, 1]. Definition 2. The international standard and GOST R ISO 9000-2001 use the terms validity or invalidity for assessing the quality of works, rendered services, produced goods and systems of management. Definition 3. The invalidity of a system is a deviation of its state from the state given by technical requirements and specifications. The invalidity of a parameter or a factor of a system is a deviation of its value from the set or the standard value. Definition 4. The invalidity of a state is considered as an eventproposition, which corresponds to a logical variable. The degree or characteristics of invalidity have different values in the range [0, 1] and are considered a system state risk. Definition 5. The invalidity of a system as an event is calculated by the invalidity of its events-parameters. Definition 6. If a parameter is constant, then it is not viewed as an event in the system state. For example, “the number of women” is a constant parameter in the current state of SES “Birth rate in the country”. This parameter is not introduced in the LP-risk model. Definition 7. The number of risk initiating indexes is substantially less than the number of parameters describing a system’s state. Definition 8. “Risk management technologies” with LP-risk models are employed. They view risk and efficiency as a single entity. The mathematical expectation of losses is calculated as the product of risk and system assets value. Definition 9. The SES LP-risk model allows one to assess, analyze, predict and manage system risk, allocating resources for reducing the risk of initiating parameters.

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Definition 10. The management of an economy can be improved, if, together with the problems of micro- and macroeconomics, we solve the problems of the management of economic safety of SES of groups SES-1, SES-2 and SES-3. Definition 11. LP-risk models of the state of different SES can be combined into one model by logical operations AND, OR, NOT. The following restrictions exist in top-economics: 1. We should select the most important events as initiating events (IE) in socioeconomic systems. It is not required to describe events in a system in detail. In considered applications the number of IE is not more than 20. 2. A failure (reliability) of a technical system depends on the failure of certain elements of it (IE). The invalidity of an economic system is not a failure but a quality of a system. An invalid system can have all IE invalid but it still works and is still in demand because the deterioration of a system’s quality is compensated, for example, by a lower price in the market. 3. An invalid event has an invalidity measure which is considered as the probability (risk) of an invalid state. In the model of the system’s invalidity we assume that IEs are independent. 4. A decision-making person manages an invalid system by distributing the resources in order to reduce IE invalidity, taking into account the IE contributions to the system’s invalidity and their significance in the market.

1.3. Advantages and Features of Top-economics Top-economics or economic safety management has the following features and advantages: 1. Economic safety is carried out by the criterion of risk with the assessment of potential losses. 2. New types of LP-risk models can be used for each SES for comprehensive analysis and management of economic safety. 3. Top-economics has an interdisciplinary nature, as it deals with the economic, social, organizational, legal, information and logical probabilistic aspects of SES safety management. 4. Unlike classical reliability theory in engineering, where the states of system elements have only two values (failure and non-failure), the state of the system’s invalidity has many values (multi-state).

6

Chapter One

The probability of system state invalidity as an event corresponds to the values of invalidity states of its elements. 5. SES economic safety management has a complex nature, as it depends on the government, several ministries and legal bodies. Due to its complex nature there are certain difficulties in SES economic safety management. 6. The connection of LP-risk models of the states of various SES is performed via repeated initiating events (IE), which are part of LPrisk models of different SES. 7. The dynamics of the LP-risk models of SES is achieved by the correction of IE probabilities in the following cases: the emergence of new statistical data about system states; the emergence of signal events connected with changes in the economy, in politics, in law, and the arrival of innovations; a change of the situation in the world market; reforms in education, science and economy. 8. Construction of LP-risk model by parameters of one system state. 9. We use risk management technologies with logical probabilistic models which are informational, intellectual and innovative [7]. 10. An advantage of top-economics is the transparency of its methods, models and technologies.

1.4. Boolean Events-propositions in Economic Safety We extend the concept of a Boolean “event-proposition” with the aim of building LP-models of risk management and efficiency in SES and processes. New types of “events-propositions” have been introduced: the events of subjects’ failure, signaling events, invalid events, conceptual events, indicative events, etc. I. A. Ryabinin in [9, 10] evaluated the contribution of outstanding scientists G. Boole, P. Poretsky, S. Bernstein, A. Kolmogorov and V. Glivenko in the foundations of LP-calculus. The uniqueness of LPcalculus consists in the fact that it is not considered an academic discipline in mathematical handbooks, although it is used in many applications. Boole’s axioms of propositions logic. In 1840 the English scientist George Boole published the paper in which he introduced the evaluation of the truthfulness of expressions, or Boolean algebra. This work laid the foundations of the new academic discipline - mathematical logic. In mathematical logic a sentence is understood as any expression which can be said to be true or false. The notation A and B is a sentence whose truthfulness equals the truthfulness of both sentences A and B. The notation A or ȼ is the sentence, whose truthfulness equals the truthfulness

Scientific Foundations of Top-economics

7

of at least one of the sentences A or B. The negation of sentence A is also used. Notation U is a sentence which is always true. Notation V is a sentence which is always false. A set of sentences is a normalized Boolean algebra with the simplest possible norm. Here each sentence A is assigned “a logical value”, which equals 1 or 0, depending on whether this sentence is true or false. Bernstein’s axiomatic of events. In 1917 the Russian scientist S. N. Bernstein published a paper in which he applied the sentence axiomatic from Boolean logic to events axioms. He described a set of thirteen sentences which he viewed as the axiomatic description of the notion of an event and introduced the probabilities of events. In this case there was no longer a necessity to formulate the special axiomatic for the notion of “an event”, and a ready-made axiomatic of sentences was used. Such statement of a question is quite valid, because every event A can be said to correspond to the sentence “event Ⱥ is happening” (in the past, present or future). Obviously, it does not matter whether we talk about the probability of event A or about the truth probability of the said sentence. The probability of the sentence’s truthfulness has the same formal features as the logical meaning of the sentence, but it can have not only the two values 1 and 0, but also the whole value continuum between 0 and 1. Bernstein’s events-sentences axioms are widely used in the theory of reliability and safety in engineering, but they have been ignored in economics. Kolmogorov’s axioms of probabilities. Normalized Boolean algebra of measured subsets of segment [0, 1] became the model for building the axiomatic of probabilities. This axiomatic was proposed by Ⱥ. N. Kolmogorov (1929). Probability was viewed as one of the possible measures. In all cases when we talk about the study of random values and a random value occurs at certain sets of points on the number scale it can be called an event; and these events must be considered as the sets of “elementary events”. Ⱥ. N. Ʉɨlmogorov’s last book, the introduction to mathematical logic, was written when he was the chair of mathematical logic in Moscow University. Glivenko’s axioms of sets. In 1939 the Russian scientist V.I. Glivenko published an article in which he analyzed and summarized the axiomatic of sentences, events and probabilities. He proved that there was no longer a need to formulate a special axiomatic not only for the notion of “event”, but also for the notion of “probability” itself: one could use the readymade axiomatic of sets and measures. Events are considered on the elements of the sets.

8

Chapter One

Professor I. Ⱥ. Ryabinin used the concepts of LP-calculus for building and analyzing LP-risk models of reliability and safety in engineering based on standard axioms of logic, events, probabilities and sets. They are based on the following concepts [9]: x events have only two levels of value (0 and 1); x events are connected by logical links AND, OR and NOT; they can have cycles and repeated events; x LP-risk models are built according to the scheme of system performance as the shortest paths of successful performance or minimal cut sets of failures; x the probability of a system’s reliability or safety is calculated; x the significance and contributions of initiating events are calculated analytically; x any L-function is reduced to the orthogonal form and replaced with a P-function (P-polynomial), on which the numerical calculation is performed. Platon Sergeevich Poretsky, the Russian mathematician and logician, was the pioneer of LP-analysis. In his work “The solution of the general problem from the probabilities’ theory with the help of mathematical logic” (1886) he scientifically shaped Boole’s idea about the applicability theory [11]. He produced the definition of LP-analysis. “From here a general path opens to the definitions of probabilities: we should find the logical connection between the event, whose probability we are looking for, and other events, the probabilities of which are given. Then a transition should be made from the logical equality of events to the algebraic equality of their probabilities”. We have broadened the notion of an “event” in “Risk management technologies in structurally complex systems” on the basis of the mentioned axioms and rules of mathematical logic. New types of events have been introduced, which are propositions and have the probabilities of truthfulness. The combination of sentences (propositions) forms a complex derivative of an event. Actually, the provisions of various state standards, instructions, requirements and forecasts are formulated as sentences, having the probability of truthfulness, success or danger [12, 13]. In the tasks of SES economic safety management by risk and efficiency criteria instead of probabilities of truthfulness/falseness of events the probabilities of success/failure and danger/non-danger of events are used. The probabilities of events-propositions are essentially the elements of fuzzy logic, used in inference engines in expert systems [15].

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1. Events-propositions about the failure of the subjects. For assessment, analysis, forecasting and management of complicated socioeconomic problems we propose hybrid LP-risk models, which are built as logical functions of events-propositions about the failure of eventssubjects and events-objects. The complicated problems are the ones which are solved by the subjects and which also contain a number of objects (tasks) constituting the core of the problem [7, 8]. An event-subject is the failure of a subject to solve a difficult problem. Such events-subjects include the State, business, banks, scientists and public opinion. Events-propositions about the subjects’ failure include: x the failure of the State to solve the problem, x the failure of business to solve the problem, x the failure of the banks to solve the problem, x the failure of the scientists to solve the problem, x the failure of public opinion to solve the problem. 2. Signal events-propositions. Let significant events-propositions in economy, politics, law, innovations, etc. be called signal events for changing the probabilities of initiating events in LP-models of SES risk. We will make use only of the fact of the emergence of a signal eventproposition. Let us analyze the following signal events-propositions: x in economy, x in politics, x in law, x in innovations (the introduction of new types of equipment, service, etc.), x in natural disasters and wars, x in the changing situation in the world market. Probabilities of IE are corrected by non-numerical, inexact and incomplete (NII) expert information, based on N.V. Hovanov’s randomized aggregates method [14]. 3. Events-propositions of invalidity. An invalid event-proposition is the deviation of qi factor from zero or a set value. The indexes are normalized and have their values in the interval [0, 1]. The sentence, that the value of factor qi t 0, (1) is an event-proposition of invalidity. The probability of an eventproposition equals the value of the factor itself.

10

Chapter One

4. Conceptual events-propositions. Conceptual events-propositions are the forecast of evolution. The probabilities of conceptual eventspropositions are the probabilities of the truthfulness of propositions or forecasts. Let us assess them by NII-expert information [14]. Note that the notion of the conceptual event-proposition is the first one in Boolean logic. Actually, the provisions of various standards, instructions and forecasts are formulated as propositions, to which we can assign the probabilities of truthfulness, success or danger. 5. Indicative events-propositions are formulated as sentences and viewed as invalid events. Their measure is the deviation of the parameter from the set value. The probabilities of indicative events-propositions are the measure of danger of system parameters. 6. Events-propositions concerning latency. The probabilities of latent events-propositions are assessed indirectly by the results of public opinion polls and by social networks analysis. 7. Incompatible events. Incompatible events groups (IEG) in LP-risk models were introduced by A. S. Mozhaev for events describing the reliability of a technical system [16]. They can be called “horizontal” IEG. IEG for the grades of parameters were introduced in SES. They can be called “vertical”. Examples of LP-risk models with events-propositions. Examples are as instructive as theory. Examples of the application of eventspropositions in LP-risk models of SES and processes are described in [7, 8, 13, 17, 18]. They refer to the following LP-models: counteraction to corruption and bribery, failure risk of the development of Russia, the management of the innovations’ system in the country etc. In Chapter 2 the reader will find detailed descriptions of these and other LP-risk models.

1.5. New Types of LP-risk Models The following new types of LP-risk models in socioeconomic systems are discussed [7, 8, 13]: 1. Hybrid LP-risk models of the failure to manage complex socioeconomic systems; they are built on the basis of risk scenario for the subjects taking part in the solution of the problem, and risk scenario for the objects-tasks constituting the core of the problem. 2. Invalid LP-risk models; they are built by invalid events.

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3. Conceptual LP-models forecasting system risk; they are built on the basis of the descriptions of specialists who can understand the nature of the problem. 4. Indicative LP-risk models of system state danger; they are built by indicative indexes. The above mentioned new types of risk models are part of the system of the management of socioeconomic systems of groups SES-1, SES-2 and SES-3. All these new types of LP-risk models can be used for one SES for comprehensive analysis and management of socioeconomic safety.

1.5.1. Hybrid LP-risk Model of Risk of Failure to Solve Difficult Problems The works [7, 20, 21] deal with scenarios of risk models of the failure to solve a number of difficult socioeconomic problems: counteraction to corruption and bribery, counteraction to drug addiction in the regions, operation risks and capital reservation management, etc. Let us describe the construction of hybrid LP-models for assessment and analysis of the risk of failure to solve complex problems through the example of the management of the system of innovations of the country. LP-risk models of the failure to solve complex problems include the scenarios of the failure of the subjects (the State, business, banks, scientists and public opinion) taking part in the solution of the problems, and the scenarios of the failure of the objects-tasks constituting the core of the problems. An event of a subject’s failure is represented as the logical addition of the events “Lack of wish” and “Lack of opportunities”. Certain subjects do not wish to solve the problem. The Nobel Prize winner J. Buchanan demonstrated that the State tends to merge with corruption and crime, as it has no financial and human resources to solve all the problems. In order to make the government work for the sake of people we need the wishes and opportunities of public opinion (represented by opposition, democratic institutions, newspapers and TV). Public opinion can also be represented by the results of sociological research, lawmakers’ requests, demonstrations, etc. The hybrid LP-risk model combines the scenarios of both subjects and objects. The failure to solve a difficult problem DPinn depends on the subjects Sinn(S1,…,S5) taking part in the solution of the problem and tasks Tinn (T1, T2, T3), constituting the essence of the problem (Fig. 1).

Chapter One

12

Subjects: S1 - the State (President, the Government, the State Duma, the Federation Council); S2 - business; S3 - banks; S4 - scientists; S5 public opinion. The subjects have wishes W and opportunities O to solve the problem. Objects-tasks: T1 - monitoring of the system of innovations features; T2 - the construction of the conceptual LP-risk forecasting model; and T3 - the construction of the indicative LP-model forecasting the danger of the system of innovations state. In Fig. 1 in problems Tinn the following notation is used: SC - the scenario of the problem solution risk, LM -the logical risk model, PM -the probabilistic risk model. Events-propositions and logical variables are connected with objects and subjects DPinn, Sinn, S1, …,S5, Tinn, T1, T2, T3. Let us denote them by the same identifiers. The logical functions of the innovations system failure in the country are:

Siin š Tinn ; Sinn

DPinn

S1 › ... › S5 ; Tiin

T1 › T2 › T3 ,

(2)

where Sinn – the derivative of the subjects’ failure event and Tinn - the derivative of the objects’ failure event. The probabilistic model of the innovations system failure in the country is as follows:

P{DPiin

0} P{S inn

0}˜ P{Tinn

0};

(3)

P^Sinn = 0`= P^S1 = 0`+ P^S 2 = 0`( 1  P^S1 = 0`) + P^S3 = 0`( 1  P^S1 = 0`)( 1  P^S 2 = 0`) + ...; P{Tinn

0}

P{T1

0}  P{T2

0} (1  P{T1

0})  P{T3

0} (1  P{T1

0})(1  P{T2

0})  ... .

The probabilities of events-propositions S1,...., S5, T1, T2, T3 are assessed by the randomized aggregates method by non-numerical, inaccurate and incomplete information [14].

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Fig. 1. Hybrid LP-risk model of the failure

Risk scenarios for the subjects of LP-models are created, which take into account their wishes and opportunities as events. For risk models of objects-tasks, structural, logical and probabilistic risk models are developed. Let us describe the scenarios for the subjects participating in the solution of the innovations problem, scenarios which we will use for building the LP-models of failure and for assessing the probabilities of events by expert information. The State S1 expresses its wish W1 to solve a problem by numerous declarations of its leaders and by creating decrees and committees. The opportunities O1 to solve a problem are limited due to the lack of resources, specialists, ideas and knowledge about risk management technologies. Business S2 has a wish W2 to make as much money as possible, as fast as possible, by all possible means and to survive the competition. Business will support only those innovations which will bring it a lot of benefits in the short-term perspective. The State as a regulator can oblige business to transfer some of the profit to the innovations fund. Banks S3. Wish W3 of banks is to make as much money as possible and to survive the competition. Banks are interested in giving loans for innovations, which might bring them a lot of profits without any risk. The

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Chapter One

State as a regulator can make banks transfer some of their profits to the innovations fund. Scientists S4 have built hybrid, conceptual and indicative LP-risk models, as well as the corresponding software complexes. Public opinion S5 has wish W5 to solve the innovations problem in the country. It might induce the State, business and banks to develop and implement the innovations system. It realizes its opportunities O5 through democratic institutions, opposition, mass media, lawmakers’ requests, meetings, demonstrations, etc. The simulation of the risk of the failure to solve difficult problems demonstrated that it is impossible to solve difficult problems in Russia without scientists and public opinion.

1.5.2. LP-models of Invalidity of Socioeconomic Systems Standard ISO 9001 – 2001 defines the invalidity of SES, processes and goods as the failure of their parameters to correspond to certain norms and regulations. The assessment of economic systems’ performance and the assessment of products is the statutory requirement of WTO. LP-risk models of the invalidity of systems and processes belong to the class of models “LP-modeling”. S. W. Bogoslovsky [22] was the author of the first work devoted to the assessment of the invalidity of economic processes on the basis of LPmodeling. However, it lacks any section devoted to the construction of models, and all examples have been taken from engineering. It describes only the well-known expansion of the L-function by the list of its arguments [9]. It is for the first time that LP-risk models of SES invalidity, processes and products have been developed. The development of the invalidity scenario is a creative process. Only a specialist with a deep knowledge of system performance can define the total number of invalid states. Chapter 2 presents our technique of building LP-models of invalidity for the assessment of systems, processes and goods quality in accordance with WTO requirements.

1.5.3. Conceptual LP-risk Models of Forecasting of Invalidity On the basis of informal descriptions from [23] we have created specific scenario conceptual LP-models of risk development forecast through the example of drug addiction in a region. We have proposed a

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conceptual LP-model which predicts the development of drug addiction in a region and combines separate LP-risk models. The conceptual LP-model which predicts the risk of the development process is the logical integration of influencing events-indexes, which are not quantitative. Let us use expert information to assess the risks of events-propositions regarding drug addiction development [14]. The conceptual LP-model forecasting the risk of every process can be verbally formulated as follows: the risk of drug addiction development grows due to any single factor or due to any two indexes, or due to all indexes. 1. The LP-model forecasting the risk of drug addiction development due to deterioration of moral values: Y1 = Z1 › Z 2 › Z 3 › Z 4 › Z 5 , (4) where Z1 – poor heredity; Z2 – poor upbringing in the family; Z3 – inability to realize that you have really become a drug addict; Z4 – lack of motivation for productive activities; Z5 – lack of spiritual and ethical values; › – the operation of logical addition. The probabilistic model forecasting the risk of drug addiction development: P^Y1`= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ) + ... (5) 2. The LP-model forecasting the risk of drug addiction development due to the failure to counteract it:

Y2 = Z1 › Z 2 › Z 3 , where Z1 – inefficiency of law-enforcement authorities’ actions aimed at counteraction of proliferation of drugs and illegal drug trafficking; Z2 – inefficiency of drug abuse prevention in order to develop certain resistance to drug addiction; Z3 – inefficiency of the authorities’ actions aimed at the improvement of the socioeconomic situation in the region. The probabilistic model of drug abuse growth risk:

P^Y2 `= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ). 3. The LP-model forecasting the risk of drug addiction development due to the deterioration of the demographic situation:

Y3 = Z1 › Z 2 › Z 3 › Z 4 › Z 5 , where Z1 – deterioration of survival conditions in the area during a crisis; Z2 – deterioration of the protection of the vital interests of the area; Z3 –

Chapter One

16

deterioration of immunity and outward defenses from destabilizing indexes; Z4 – competition decrease in an economy, lack of economic stability; Z5 – deterioration of decent living conditions and sustainable development of a personality. The probabilistic model forecasting drug abuse growth risk looks as follows:

P^Y3 `= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ) + ... 4. The LP-model forecasting the risk of drug addiction development due to drugs proliferation:

Y4 = Z1 › Z 2 › Z 3 , where Z1 – deterioration of resistance to drugs; Z2 – deterioration in the counteraction to illegal drug trafficking and narcotic substances withdrawal; Z3 – deterioration of social, economic and political indexes affecting the growth of risk groups. The probabilistic model forecasting the risk of drug addiction growth:

P^Y4 `= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ). 5. The LP-model forecasting drug addiction risk due to the influence of drug abuse on the development of society:

Y5 = Z1 › Z 2 › Z 3 › Z 4 › Z 5 › Z 6 › Z 7 , where Z1 – economic risk growth in the region due to unemployment, redundancies, salaries delays, etc.; Z2 – risk groups growth due to the fact that the unemployed are actually potential drug addicts; Z3 – alcoholism and drug addiction growth within the framework of risk groups; Z4 – risk groups’ growth due to the arrival of psychologically vulnerable groups of society – college and university students and minors who live in hostels and orphan asylums; Z5 – decrease in the number of young people; Z6 – decrease of workforce in the economy, fall in the production of goods in the area; Z7 – replacement of locals with migrant workers. The probabilistic model forecasting drug addiction development risk:

P^Y5 `= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ) + ... 6. The LP-model forecasting the risk of drug addiction growth due to the risk of trying drugs for the first time:

Y6 = Z 1 › Z 2 › Z 3 . Here: Z1 – psychological readiness growth; Z2 – drug availability in the area; Z3 – increase of unsolved crimes of this type; Z11 – a person's

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17

psychological readiness growth; Z12 – psychological readiness growth (support of the environment) which in its turn is the derivative of an event Z11 which has initiating events; Z111 – escaping a hard real-life situation; Z112 – status growth in certain circles; Z113 – no difference is perceived between the notions “to take drugs” and “not to take drugs”; Z121 – lack of career growth perspectives; Z122 – promotion of drugs and the way of life of drug addicts; Z123 – lack of administrative measures; Z124 – availability of drugs and drug dealers in night clubs and similar places. Initiating events Z1, Z2,…; Z124 have no quantitative values. Their risks R1, R2,…, R124 should be evaluated by expert information [14]. The conceptual L-model forecasting the risk of drug addiction growth in a region is the logical sum of separate conceptual processes Y1,…,Y6:

Y = Y1 › Y2 › Y3 › Y4 › Y5 › Y6 .

(6)

The conceptual P-model forecasting the risk of drug addiction growth in a region:

P^Y `= Py1 + Py2 (1  Py1 ) + Py3 (1  Py2 )(1  Py1 ) + .....

(7)

1.5.4. Indicative LP-risk Models of the System’s Danger State Indicative LP-models of the danger of the system state were introduced and described in [13, 20]. The states of SES systems are usually described by a set of indexes. For example, the state of a country's innovations system can be described by 84 indexes [24], the state of drug addiction in a country or a region is described by 40 indexes [20]. The sets of indexes allow us to compare different countries and measure their ratings. The indexes are divided into the groups of the first level (there are 5-7 of them). Each group has several separate indexes. Each factor of the group, in its turn has some initial indexes. The groups have quite clear functions. For example, five groups of indexes assess the opportunities of the innovations system: 1. Institutions - the State (political environment, regulation of the environment, business-environment). 2. Human capital assets and research (education, science and development). 3. Infrastructure (information technologies, etc.). 4. Market (loans, investments, trade and competition).

18

Chapter One

5. Business (employees’ skills, the connection of business with innovations, knowledge implementation). Two groups of indexes evaluate the results of the innovations system: 6. Scientific research results. 7. Creative research results. Every factor has a certain meaning in absolute and relative terms. The indexes in the problems of innovations and drug addiction and LP-risk models are dealt with in Chapter 2. Thus, there are a lot of indexes for the description of a system, but not all of them can be the indicators of system danger. Therefore we should build the indicative indexes which characterize system danger and define the other aspect of the problems – what must be done? The indicative LP-model of drug abuse danger. The indexes of drug abuse in a region characterize the current state of the problem and of counteraction to the proliferation of drugs, but they do not specify the risk of drug abuse danger which should be used for controlling the state of drug addiction. Drug abuse indexes, for which we might introduce the notion of the valid event by condition (1), are initiating indicative indexes characterizing drug abuse risk. Probability or risks are the criteria of drug abuse in a region. In LPrisk models of drug abuse in a region all events can be viewed as dangerous, and this danger grows with the appearance of every new event. When the events are logically added the system risk belongs to the interval [0, 1]. Drug abuse danger decreases when the number of risk events falls and it grows when the number of events increases. Drug addiction always causes damage and losses; therefore we should talk about it in terms of risk. However, when analyzing events we talk about their probabilities. Therefore, the notions of risk and probability are used as equal to each other. The indicative LP-risk model of drug abuse danger in the region is built by the indicative indexes of groups. Indicative indexes are the derivatives of events, corresponding to logical variables. The LP-risk model of drug abuse danger in the region by indicative indexes:

Y = Y1 › Y2 › Y3 › Y4 › Y5 › Y6 ,

(8)

where Y1, Y2, …,Y6 are logical variables of derivative events for groups of indexes.

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19

The probabilities of initiating indicative indexes are assessed as the probabilities of invalid events. The indicative LP-model of the danger of the state of the innovations system of Russia. On the basis of the performed analysis of the innovation “Risk management technologies in structurally complex systems” we have determined the indicative events-propositions connected with the failure of the innovations system (Table 1). The list of events-propositions might change during the analysis of the processes of the development of other innovations. Let us use these indicative events-propositions of the innovations system’s danger risk for building the LP-risk model of the innovations system’s failure. The probabilities of indicative events-propositions are assessed by expert information. Table 1. Events-propositions about the dangerous state of the innovation system ʋ 1 2 3 4 5 6 7 8 9 10 11

Characteristic Communication with foreign scientists Identification of top-priority fundamental and applied research The concept of the development of socioeconomic systems and the country The involvement of scholars and public opinion in the solution of complex socioeconomic problems The creation of innovation projects at the confluence of sciences The adoption of foreign methods, programs and techniques The analysis of wishes and possibilities of the subjects participating in the solution of the problem Credit provision management Funding of science and innovation projects Formation of the orders bank for fundamental applied projects and research from companies and ministries The share of the country’s gross output allocated to the innovations fund and science

Indentifier Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11

The indicative LP-model of the innovations system state danger is expressed verbally as follows: a dangerous situation can occur either due

20

Chapter One

to any single event-proposition or due to any two events-propositions, or … due to all events-propositions. The indicative logical model of the innovations system state danger: Y Z1 › ... › Z11 . (9) The indicative probabilistic model of the innovations system state danger: (10) P^Y `= R1 + R2 (1  R1 ) + R3 (1  R2 )(1  R1 ) + ..., where Rn – the risks of events-indexes Zn, n=1, 2,…,11. The techniques of LP-analysis and LP-risk management in the systems are described in [7, 8]. In the simple structure of expressions (9, 10) the probabilities and contributions of initiating events-indexes Z into the innovations system failure risk are proportional to their risk value. The management consists in reducing the risk of the most significant eventspropositions by way of structural changes in economy, science, education and resources allocation. Chapter 2 deals with the following new LP-risk models of SES: 1. LP-risk models for managing the innovations system of the country. 2. LP-risk models for counteraction to bribery and corruption in the country. 3. LP-risk models for counteraction to drug addiction in the country. 4. LP-models of the operational risk of a bank and capital reservation by Basel. 5. LP-models of invalidity of systems for quality management by WTO. 6. Hybrid LP-risk models of solving difficult socioeconomic problems. 7. Logical probabilistic management of the risk of the economic situation in Russia.

1.6. Database and Knowledge Base of Socioeconomic Systems Any tabular database of a system can be transformed into a tabular knowledge base and a system of logical equations. It allows one to build an LP-risk model and solve the problems of analysis, forecasting and system risk management.

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21

1.6.1. Data Structure and Statistical Database Structural representation of data is used for modeling risk and efficiency in SES systems [7, 8]: 1) the subsystem of a system; 2) a set of states of the subsystem; 3) the state from the set of states of subsystems; 4) the parameters describing a state; 5) the grades of the parameters of the state and the efficiency parameter. The structural model of a system can be expanded “upwards” and “downwards”. In the latter case the system becomes a subsystem of a bigger system. This bigger system contains repeated IEs and events, which depend on signal events in the economy, in politics, law, innovations, natural disasters and wars. The following features of the system are considered: N – the number of system states in statistical data; n – the number of indexes affecting the efficiency parameter; N – the number of grades for the values of indexes; Ny – the number of grades for the efficiency parameter. Let us use the following notation for random events and corresponding L-variables in the problems connected with risk: Y – the efficiency parameter; Yr, r=1, 2,…,Ny – events-grades of the efficiency parameter; Z1,…,Zj, …,Zn – events-indexes; Zjr – events-grades, j=1, 2,..., n; r=1,2,...,Nj. In risk scenarios events-indexes are linked by L-connections OR, AND, NOT. Events-grades for each index make an incompatible events group (IEG). The largest number of various system states equals:

N max = N1 ˜ N 2 ˜ ... ˜ N j ˜ ... ˜ N n ,

(11)

where N1,…,Nj,…,Nn are the numbers of grades in indexes. A database of the tabular type (Table 2) contains statistical information about similar objects or states of a system at different points in time. In the table the number of columns can reach several dozens, and the number of rows - several hundreds. The values of indexes can be quantitative and qualitative, discrete and continuous. The indexes of the database can have an infinitely large set of values.

Chapter One

22

Table 2. The database -- system states and the values of indexes State 1 … I … N

Index, A1 A11 … Ai1 … AN1

…

Index, Aj A1j … Aij … ANj

… … … … …

… … … … … …

Index, An A1n … Ain

Parameter of Efficiency, Ei E1 … Ei

ANn

EN

In the cells of the table we can find the values of the indexes of the state. We can use quantitative and qualitative scales in order to measure them. The last column of the table is the efficiency parameter. Let us denote the indexes as A1,...,,Aj,…, An, and the efficiency parameter – Ei, i=1,…,N. The values of indexes Aij are in the cells of Table 2 and for the last column – of parameter Ei.

1.6.2. Events-parameters and Events-grades Let us alter the representation of the database and substitute the values of indexes by their grades (numbered intervals) and denote the variables. Efficiency parameter E takes values from the set E1,...,Er,...,Em. Variable E depends on A1,…,Aj,…,An. Variable Aj takes values (grades) from the set Aj1,…, Ajr,…,AjNj. The statistical data are represented by the table, the i-th row of which looks as follows:

Ari1 ,..., Ari 2 ,..., Arni , Eri , where:

^1 , 2 , . . . , N ` ; r  ^1 , 2 , . . . , N 1 ` ;

i r1

rj 

^1 , 2 , . . . , N

^1 , 2 , . . . , N i ` ; r 2  ^1 , 2 , . . . , N 2 ` ; j ` ; r n  ^1 , 2 , . . . , N n ` . 

Let us introduce random events (Table 3). Event Zjr happens when variable Aj for the random i-th row takes the value Ajr =Zjr; Aj=Ajr. The probability of this event: P(Zjr)=P(Aj=Ajr). Event Yr happens when variable E for the random i-th row takes the value Er: Yr=Er. The probability of the event: P(Yr)=P(E=Er).

Scientific Foundations of Top-economics

23

Let us match events Zjr, j=1,…,n; r=1, …,Nj and Yr, r=1,…,Ny with Lvariables with the same identifiers. Let us also introduce events Z1,…,Zn and Y, each of which contains a group of incompatible events: Z j Z j1 ,..., Z jr ,..., Z jNj , j 1,2,..., n; Y Y1 ,..., Yr ,..., YNy . (12) Thus, in Table 3, each event-index has a set with a finite number of events-grades.

1.6.3. The Transition from the Database to Table Knowledge Base Statistics knows everything. Statistics is knowledge itself if we pose the correct questions and get rid of the “course” of an infinitely large number of values, which is poorly perceived and is hardly suitable for calculations. Let us change the representation of the database [7] and replace the indexes with the values of grades (numbered intervals) and introduce the values of variables. Now in each cell of the table there is an event-grade Zjr , j=1,2,…,n; r=1,2,…,Nj (Table 3). Event-grade Yr, r=1,2,…,Ny is in the cell of the column for the efficiency parameter. For each event-grade we simply have to calculate the frequency of its occurrence in statistical data. Let us consider two different events for system states in the statistical tabular knowledge base: 1) event occurrence state – Y2; 2) event failure state – Y. Table 3. States, events and L-variables Stateevent 1 … I … N

Event, Z1 Z11r1 … Zi1r1 … ZN1r1

…

Event, Zj Zjjrj … Zijrj … ZNjrj

…

Event, Zn Z1nrn … Zinrn

Event, Yr Y1ry … Yiry

ZNnrn

YNry

L-function of the occurrence of state Y2 in statistical data:

Y2 = Z 1 š Z 2 š ... š Z j š ...Z n ,

(13)

24

Chapter One

where Z1, Z2,…,Zn are L-variables of state parameters. The lower index Y denotes the occurrence of an event and gives parameters Z1, Z2,…,Zn the sense of influence on the event occurrence. Logical variable Y2 has value 1 for the occurrence of the state. Logical variable Y2 has value 0 for the event non-occurrence of the state. Using (12), let us write down the P-function of state occurrence in statistics (14) P (Y2 1) P 21 ˜ P 22 ˜ ... ˜ P 2 j ˜ ... ˜ P 2n , where P2j = P{Zj} is the probability of event Zj occurrence. L-risk function of state Y failure in statistical data will be written down as: Y = Z 1 › Z 2 › ... › Z j › ...Z n , (15) where Z1, Z2,…,Zn are L-variables of indexes of the state. Logical function Y denotes the failure of the event and gives indexes Z1, Z2,…,Zn the sense of influencing the failure of event Y. L-function of the failure of system Y states can be of any L-complexity and have connections OR, AND, NOT, as well as cycles. L-function of state (13) failure in the orthogonal form: Y = Z 1 › Z 2 Z 1 › Z 3 Z 2 Z 1 › .... (16) Orthogonality means: the product of any L-items in (16) equals zero. It allows us to make a transition from logic to arithmetic and write down the P-function of state failure: (17) P(Y 0) = P1 + P2 (1  P1 ) + P3 (1  P2 )(1  P1 ) +..., where Pj=P{Zj} – the probability that independent events Zj lead to success Y. The criteria of risk models quality bearing such exotic names as the criteria of “fascination”, “weirdness”, GENIE, etc. are built by graphs in the coordinates “the probability of state occurrence – the risk of state failure”.

1.6.4. The Knowledge Base and the System of L-equations According to (15), the system of L-equations by statistical data (Table 3) for the failure of system states will be written down as:

Scientific Foundations of Top-economics 1 ­ Z 11r1 › ... › Z 1 jri › ... › Z nrn = Yry1 ; ° °... ... ... ... ° i i i i ® Z 1r1 › ... › Z jri › ... › Z nrn = Yry ; °... ... ... ... ° N ° Z N 1r1 › ... › Z N jri › ... › Z nrn = YryN . ¯

25

(18)

Let us call system (18) a knowledge base (KB), treat it as a system of L-expressions and use it for obtaining new knowledge. For (18), taking into account (17), let us write down the system of P-equations for the failure of system states:

­ P11r1  P12 r 2 (1  P11r1 )  P13r 3 (1  P11r1 )(1  P12 r 2 )  ... = P(Y 1 0) ; ° °... ... ... ... ° i i i i i i i 0) ; ® P 1r1  P 2 r 2 (1  P 1r1 )  P 3r 3 (1  P 1r1 )(1  P 2 r 2 )  ... = P(Y ° °... ... ... ... ° P N 1r1  P N 2 r 2 (1  P N 1r1 )  P N 3r 3 (1  P N 1r1 )(1  P N 2 r 2 )  ... = P (Y N 0) . ¯ (19)

1.7. Incompatible Events Groups Incompatible events groups (IEG) are introduced for the grades of SES parameters in LP-risk models of classes “LP-classification” (credit risk assessment) and “LP-efficiency” (forecasting the risk of investment portfolio and the efficiency of a factory) [7, 17]. The system state can be described by parameters Z1,Z2,…,Zn. Each parameter has a number of events-grades. These events-grades form the group of incompatible events (Fig. 2).

1.7.1. Logic and Probabilities in Incompatible Events Groups The following logical identical equations hold true for events-grades in IEG [9, 16]:

26

Chapter One

z jr š z jk = 0; z jr › z jk = 1; z jr š z jk = z jk ;

(20)

z jr › z jk = z jk .

Fig.2. Probabilities in the groups of incompatible events

Substitution rules of incompatible events-grades of their probabilities hold true in IEG:

Scientific Foundations of Top-economics

­ P( z jr š z jk ) = 0; ° ° P( z jr › z jk ) = 1; ® ° P( z jr › z jk ) = P( z jr ) + P( z jk ) = P2 jr + P2 jk ; ° P( z š z ) = 1  ( P( z ) + P( z )) = 1  ( P2 + P2 ). jr jk jr jk jr jk ¯

27

(21)

Logic and probabilities in IEG for states failure. For each IEG we should consider the following three probabilities of events-grades Zjr: P2jr – the frequency of statistical data occurrence in the states; P1jr – the probability in IEG; Pjr – the probability of event-grade Zjr causing the risk of system Y. The probabilities for IEG are defined as follows [7, 17]:

P2 jr = P( z jr ); ¦ P2 jr = 1, r = 1,2 ,..., N j ; Pjr = P( z jr ) |Y =0 , r = 1,2,..., N j ; P1 jr = Pjr / ¦ Pjr ;

¦ P1

jr

(22)

= 1, r = 1,2,..., N j .

Average probabilities in IEG equal:

­ ° P2 jm = 1 / N j ; ° Nj °° ® Pjm = ¦ Pjr P2 jr ; r =1 ° Nj ° ° P1jm = ¦ P1jr P2 jr . °¯ r =1

(23)

We have to substitute L-variables Zjr, j=1,2,…,n, r=1,2,…,Nj with Lvariables Z1,…, Zj,…, Zn for the events-grades of this very state i in the logical risk function of i-state of the system. The probability of eventparameter Zj equals the probability of one of the events Zjr from IEG, i.e. P(Zjr|Y=0)=Pjr. We have to substitute L-variables Zjr, j=1,2. We have to substitute Lvariables Zjr, j=1,2,…,n, r=1,2,…,Nj with L-variables Z+1,…,Zj,…,Zn for the events-grades of this very state i in the logical risk function of i-state of the system. The probability of event-parameter Zj equals the probability of one of the events Zjr from IEG, i.e. P(Zjr|Y=0)=Pjr.

Chapter One

28

1.7.2. The Bayes Formula for Probabilities in Incompatible Events Groups The probabilities Pjr are assessed during algorithmic iterative training of the ȼ-risk model by statistical data. First, we have to find probabilities P1jr, which hold true for (22), and make a transition from P1jr to probabilities Pjr. The number of independent probabilities Pjr equals n

N ind = (¦ N j )  n .

(24)

j=1

Probabilities Pjr, P1jr, P2jr, Pjm, P1jm and P2jm are connected by the Bayes formula. This connection is used when LP-risk models are trained by statistical data. The identification (optimization) problem is solved by the iterative method. One cannot actually talk here of a prior and a posterior probability. The Bayes formula can be formally written down as regard to P1jr versus Pjr or, vice versa, as regard to Pjr versus P1jr. For the purpose of iterative optimization (training) of the P-risk model the Bayes formula could be written down as follows:

Pjr = P1jr

Pjm P2 jr

,r = 1,2,...,N j , j = 1,2,...,n.

(25)

This allows us to generate one independent probability P1jr less in IEG than while generating independent probabilities Pjr. In this way we can also simplify the assessment of the accuracy of probabilities P1jr in IEG, as their sum in IEG equals 1. Certain difficulties arise in application of the Bayes formula, because due to the limited amount of statistical data zero or a very small value could be a denominator in (25). Therefore, we propose to link probabilities Pjr and P1jr by the following modification of the Bayes formula, using the mean values of probabilities P2jr [7, 19]:

Pjr = P1jr

Pjm P2 jm

,r = 1,2 ,...,N j , j = 1,2,...,n.

(26)

1.8. Risk Management Technologies in Structure-complex Systems (SCS) For more than ten years the laboratory “CAD Integrated Systems” of the Institute of the Problems of Mechanical Engineering (IPME RAS)

Scientific Foundations of Top-economics

29

has been conducting fundamental and applied research on risk management technologies in structurally complex systems. Its results have been published in Russia and abroad and are used in the training of economics undergraduates in St. Petersburg State University of Aerospace Instrumentation. First, LP-risk models for some applications in engineering and economy were created, then, finally, we realized that we needed risk management technologies in structurally complex systems [7, 13]. The theoretical importance and practical relevance of our work is determined by the urgent need to develop adequate models for SES economic safety management, models which would have common methodological grounds, models which are absolutely vital for the sustainable development of Russia. Such SES include: management of SES and the safety of the country’s state and development, counteraction to bribery and corruption, counteraction to drug addiction, management of the system of innovations in the country, management of the systems of credit and operational risks of banks, etc. The following famous scientists influenced the development of models, techniques, technologies, tasks and risk management objects: N. Wiener and J. Neumann, who believed that SES management methods must be based on combinatorics, logic and sets [25, 26]; R. Kalman, who wrote that the problem “data - the model, explaining the data should be treated as the main one for any branch of science” [27]; I. Ryabinin, who introduced LP-calculus for risk analysis in engineering systems [9]; the Nobel Prize winner James Buchanan, who studied the model of the sustainable development of States on the basis of taken economic and political decisions [2]; the Nobel Prize winner James Heckman, the author of the theory of analysis of micro data, dissimilarities and politics assessment on the basis of socioeconomic processes statistics [3].

1.8.1. Components of Risk Management Technologies Risk management technologies (RMT) in SCS are sets of techniques, LP-models, LP-procedures, special software and examples of risk assessment and analysis [7, 18]. The system and the processes are viewed as structurally complex with random events. The events of occurrence and failure of system states are used. Events for parameters and their grades, and invalid events are introduced. In RMT in SCS risk and efficiency are treated as a whole. Risk management technologies in SCS include: x LP-calculus.

30

Chapter One

x Classes of LP-models. x Procedures for the classes of LP-models. x Special software for classes and procedures. x Examples of applications. x The training course. LP-calculus uses the extended definition of events and deals with about 10 new events-propositions. Classes of LP-risk models: x LP-modeling. x LP-classification. x LP-efficiency. x LP-forecasting. x Hybrid LP-risk models. Procedures for the classes of LP-risk models: x The construction of L-risk models. x The identification of LP-risk models by statistical data. x LP-analysis risk by significance and contributions of initiating events. x LP-risk management. x LP-forecasting of risk in the space of states. x The synthesis of the probabilities of events in LP-risk models. The examples describe more than 20 applications in economy and engineering. The training course “Risk management technologies in structurecomplex systems” lasts two semesters and includes 10 laboratory works done on the PC.

1.8.2. Classes of LP-risk Models There are five classes of LP-risk models in risk management technologies [7, 8]: LP-modeling, LP-classification, LP-efficiency, LPforecasting and hybrid LP-risk models. They have been determined on the basis of statistical data, the calculation of risk of IE and final events, the construction of LP-risk models and risk analysis and management methods. These models not only approximate statistical data, but they also explain them. There exist about forty definitions of risk in literature. Perhaps, they might be of some interest for philosophers, but it will be

Scientific Foundations of Top-economics

31

sufficient just to mention which class of LP-models it corresponds to and which event in the system it refers to. The LP-modeling class. In the LP-modeling class the final state-event of the system is considered (for example, the risk of company management failure, the risk of solving a difficult problem, the risk of an economic crisis). The probabilities of initiating events are defined by statistical data or by expert information and the risk of derivative events. A risk scenario is formulated; L- and P- risk models of failure for the final event are built. The probability of this event P is calculated by IE probabilities. An initiating event has only two meanings – 1 and 0 with probabilities Pi and Ri=1-Pi. Efficiency is calculated as the mathematical expectation of losses according to the formula E=R S, where S is possible damage and R is system risk. The contributions of IE into system risk are calculated. The construction of risk models from the LP-modeling class will be dealt with later. The LP-classification class uses the statistical data about a number of objects or system states (for example, the loans of a bank). The events of the states’ failure are considered. For each state we know the efficiency parameter, which equals 1 for good states and 0 for bad states. The statistical tabular DB is transformed into the statistical KB by the introduction of events-grades for the indexes describing the state. A system of L- and P-risk models of system failure is written down. The probabilities of events-grades are found by solving the identification problem for the system of P-risk models by statistical data. After the risk of each system state Pi is calculated, admissible risk Pad is set and average risk Pm is calculated (Fig. 3). The condition Pi < Pad divides the states into good ones (1) and bad ones (0). For all new states risk (probability) and the efficiency parameter value 1 or 0 are calculated. Frequency and probabilistic contributions of events-grades to the risk of the state, average system risk and the accuracy of LP-risk models are calculated. The construction of risk models from the LP-classification class will be described later. Good states

0

P

Bad states

P

Pb P

P

1

Fig. 3. Risk scheme for the class of LP-classification

The LP-efficiency class. It includes LP-risk models with the statistical data which are used to calculate either the efficiency parameter value (the

32

Chapter One

share’s portfolio yield), or the efficiency parameter as known from statistical data (the daily turnover of restaurants). The frequency risk analysis is conducted for these LP-models using the contributions of initiating events-grades into the tail of the efficiency parameter distribution. The states of the share’s portfolio are calculated by stock prices. For each state we know the return on shares Z1, Z2,…,Zn from the portfolio. The events of the states’ occurrence are considered. The statistical tabular DB is transformed into the tabular KB by introducing events-grades for the return on equities and the portfolio. A system of L- and P-models for the occurrence of states is written down. Portfolio yield Y is calculated for each state as a function of return on equities Z1, Z2,…,Zn and capital shares x1, x2,…,xn, invested in equities. Then the discrete distribution of portfolio yield is built (Fig. 4). The probabilities of state Yi occurrence are calculated: x by the frequencies of events-grades parameters; x by the frequencies of the efficiency parameter – by building the distribution bar chart.

Fig. 4. Risk scheme for the LP-efficiency class

In Fig. 4 the identifiers mean the following: L – the left “tail” of inadmissible yield (in the portfolio efficiency problem), R – the right “tail” for earned profit (in the company efficiency problem); Yad – minimal admissible yield; Yre – satisfactory profit. Frequency contributions of events-grades into the “tail” of risk distribution are calculated and then used for management, for example the decisions regarding the exclusion/ inclusion of new shares or the changes in their distribution in the portfolio. The LP-forecasting class. This class includes LP-risk models which use statistical data for forecasting failure risk. Forecasting is performed in

Scientific Foundations of Top-economics

33

the space of system states. The risk of the states not included in the statistical data is predicted. Admissible risk Pad of the efficiency parameter is chosen for forecasting. Risk as the tail area is calculated for the left or the right tail of the efficiency parameter distribution. For forecasting purposes, a transition is made from the LP-efficiency model to the LP-classification model (Fig. 3). To do this, states Yi < Yad are considered as good ones, and Yi > Yad – as bad ones. The identification problem is solved and the probabilities Pjr of events-grades of IE are found. The construction of the LP-forecasting model is considered in more detail in section 1.11. The class of “hybrid LP-risk models”. The hybrid LP-model is used for assessment and analysis of the risk of the failure to solve a difficult socioeconomic problem. It includes the LP-model of the LP-modeling class, which describes the behavior of events-subjects solving a problem (the State, business, banks, scientists, public opinion) and the LP-models for events-objects or the tasks constituting the core of the problem. In the hybrid LP-risk model the probabilities (risks) of events-subjects are assessed by NII expert information. The probabilities of events-objects are determined by statistical information.

1.8.3. Risk Management Technologies Procedures In risk management technologies the following procedures for the classes of LP-risk models are used [7]: the construction and orthogonalization of L-risk models; identification of LP-models by statistical data; LP-analysis of risk and efficiency; LP-management of risk and efficiency; LP-forecasting of risk and system crisis; synthesis of the probabilities of events in LP-models. The building of scenarios and LP-risk models. In order to build an LP-system risk model a scenario or a structural risk model is built, Lmodel and P-risk models are written down. An LP-risk model can always be written down as a perfect disjunctive normal form (PDNF), the most complete and cumbersome in notation and calculations. In certain cases LP-risk models with a limited number of events are built from PDNF or as the shortest operation paths or according to the risk scenario. An LP-risk model can often be set by the table of connections of the final and initiating events. An LP-risk model can be a complex one including several models which are combined by operations OR, AND, NOT. Structurally complex systems consist of several subsystems which can have several common or repeated events. An LP-risk model of failure is built taking into account

34

Chapter One

repeated events, using special algorithms of the orthogonalization of logical functions. A complex LP-risk model can be so complicated that the computer does not have enough memory to store L- and P-risk functions, or the summons in the P-function may contain many multipliers (with probabilities in the interval [0, 1]), so that the result becomes inaccurate. In this case we should build subformulae, use the decomposition of models and fold IE in the nodes of OR, AND type. The identification of LP-risk models by statistical data consists in defining admissible risk and the probabilities of the failure of initiating events-grades. An integral-valued function serves as an identification criterion function: the number of correctly recognized good and bad system states must be maximal. Identification is a reverse optimization problem, solved by algorithmic iterative methods of random search or gradients. During identification the asymmetry of recognizing good and bad states is set for the purposes of training and testing an LP-risk model. The offered methods provide a solution at any complexity level of LPmodels and for many states, parameters and grades in parameters. LP-analysis of system risk and efficiency is performed on a P-risk model. The quantitative risk analysis consists in determining the contributions of influencing events-indexes and their events-grades into the risk and efficiency of derivative system states and the system on the whole. Risk can be analyzed on the whole, for the left and the right tail and the center of the efficiency parameter distribution. Statistical and LP-methods of risk analysis have been offered. Statistical analysis is the simplest one in calculations. LP-analysis has the greatest potential for the in-depth study of risk and efficiency. Structural significance depends on the position of the event in the risk graph model. P-significance takes into account both the position and the value of the event probability. Dangerous events and combinations of events are found by the change of system risk after their exclusion. LP-management of risk and efficiency. In SES the management of system state and system development risk is usually conducted. The system state management is conducted on the basis of risk and efficiency analysis in the following order: the assessment of the contributions of events-grades and events-parameters, the selection of the most significant contributions, the allocation of resources for the change of probabilities of the most significant events-grades. The management of the system development by risk and efficiency criteria is performed through control of the movement along the chosen trajectory and corrections in case of deviations from it. The procedure of the LP-management of system risk and efficiency will be discussed later.

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LP-forecasting in space and time. A forecast is given about the risk and efficiency of system states which are not present in statistical data, i.e. in the space of states. In management, we also have to predict the risk and efficiency of a system in the time function, considering that the probabilities of initiating events change in time. For example, having identified the LP-model of loan risk using the statistical data of a bank, we can predict the risk and efficiency of new loans. A forecast of the beginning and the causes of system crisis and recession is conducted, keeping an eye on the contributions of eventsgrades to the tail of the efficiency parameter distribution. The left and the right “tails” correspondingly determine the values of the efficiency parameter Yad or Yre. The right “tail” corresponds to the recession area. The left “tail” corresponds to the area of inadmissible risk and bankruptcy. The frequencies of events-grades in the tail and the probabilities of events-grades are calculated. In order to conduct LPforecasting we have to make a transition from the LP-efficiency class model to the models of the LP-classification class. In order to make a prediction of system crisis we have to study the dynamics of contributions of events-grades in the tails of the efficiency parameter distribution. Contributions as differential characteristics can detect a system crisis better.

1.8.4. Research Topics on Risk Management Technologies Risk management technologies with LP-models reflect the nature of risk and are gaining wider applications for risk management in structurally complex systems. The classification of main research directions (Table 4) in the area of risk management in structurally complex systems simplifies the interaction of specialists and the solution of new tasks and problems. Table 4. Main research directions N

1

Procedures “Risk management technologies” Construction and ortho gonalization of LP-models

Classes of LP-models of risk and efficiency LPLPLPLPHybrid modeling classifiefficiency forecasting LPcation model 1 2 3 4 5

Chapter One

36 2 3

4 5 6

Identification of LP-models Analysis of risk and efficiency Risk management Risk prediction Synthesis of the probabilities of events

The main research directions in risk management technologies include [7, 8]: the development and research of the classes of LP-risk models, LPprocedures, technologies and software. The main research directions in risk management technologies in structurally complex systems can be classified according to the following principles: x representation of socioeconomic systems as structurally complex ones with random events, logical links and variables; x representation of initiating indexes and the efficiency parameter by the finite sets of values and their distributions – by discrete sequences; x the use of incompatible events groups; x the construction of the KB as a system of L- and P-equations; x the analysis of two event types in statistical data; x the introduction of five classes of LP-risk models; x the introduction of six procedures for technologies; x the synthesis of events probabilities by NII expert information. In economy the application area of risk management technologies is virtually boundless. For the purposes of establishing research directions in risk and efficiency management technologies the classes of LP-risk models and the procedures of risk management technologies are used. There are two types of research in risk management technologies: 1) research into each class of LP-risk models with analysis of all procedures of risk management technologies; 2) research into each procedure of risk management technologies for the classes of LP-risk and efficiency models.

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37

Thus, there are 30 minor research topics according to the number of cells (6 by 5) in Table 4 and 11 major ones: 5 topics for each class of LPmodels with the analysis of all procedures and 6 topics for each procedure, analyzed for all classes of LP-models.

1.9. Development of LP-risk Models of Socioeconomic Systems In SES, risk models of LP-modeling class are usually used. The LPrisk model from this class is built in the following order: the creation of the risk scenario, writing down the L-model by the scenario, the orthogonalization of the L-model, the transition to the P-risk model. The models of the LP-modeling class are also used for building risk models of the classes LP-classification, LP-efficiency and LP-forecasting. Let us, therefore, pay the most attention to the construction of the model of the LP-modeling class. The Swiss mathematician Rudolf Kalman determined the requirements of models in science [27]. He wrote that it might be surprising for some mathematicians that the problem “data Æ the model describing the data” should be considered as the basic one in each field of science. This requirement for the mathematical model gives us the possibility of detailed and transparent analysis of a risk model, as well as the possibility of its management. Neither scoring techniques, nor neural networks meet this requirement. The uniqueness principle emphasizes the obvious fact that scientific results must be obtained from objective data analysis and not from toying with models. LP-risk models of the LP-modeling class satisfy the Kalman rule, as well as the LP-models of the classes LP-classification, LP-efficiency and hybrid LP-risk models. The operation of LP-risk models of the LPmodeling class for various applications is discussed in [7, 8, 28].

1.9.1. Formal Methods of Development The perfect disjunctive normal form. In economics a complete set of system states can always be written down as the perfect disjunctive normal form (PDNF) with due regard to two states of each event-parameter or with due regard to the grades of each event-parameter. The number of different events-states of a system can be extremely large. Let us consider two logical functions:

38

Chapter One

Yk = Z1 š Z 2 š ... š Z jr š ... š Z n , Yk +1 = Z1 š Z 2 š ... š Z jr +1 š ... š Z n . They are orthogonal because the logic variables Zjr and Zjr + 1 belong to the same group of incompatible events: Zjr AND Zjr + 1 = 0 The L-risk model for N-states of the whole system:

Y = Y1 › Y2 › ... › Yk › ... › YN ,

(27)

where the state is defined by the L-function with all L-variables:

Yk = Z1 š Z 2 š ... š Z j š ... š Z n ,k = 1,2 ,..., N .

(28)

Each j-variable has the same number of values as the number of grades of the parameter. L-functions

Yk = Z1 š Z 2 š ... š Z jr š ... š Z n , Yk +1 = Z1 š Z 2 š ... š Z jr+1 š ... š Z n are orthogonal because Zjr and Zjr+1 belong to the incompatible events group: Zjr AND Zjr+1=0. The orthogonality of the summons of the Lfunction of system states risk allows making a transition from L-functions to algebraic risk models, analyzing the state risk by the contributions of events-grades and overcoming the computational complexity of the algorithm. The shortest paths of successful performance. The construction of LP-risk models along the shortest paths of successful performance (SPSP) is common in engineering, while there exist electric, water, gas or other schemes of a system or a device operation, etc. The LP-risk model of the system state failure is built according to the risk scenario or the graph model of risk which connects variables Z1,…,Z.n. The L-risk function is written down as the shortest paths of successful performance [9]. In order to obtain the P-risk function we have to make orthogonal the L-function; in this procedure special software and modern computers are used.

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Z3

Z1

Y

Z5

Z2

Z4

Fig. 5. Structural model of the ``bridge''

For example, the electrical circuit of the bridge type (Fig. 5) is written down in the disjunctive normal form (DNF) as a logical sum of the shortest paths of successful performance: Y = Z1 Z 3 › Z 2 Z 4 › Z1 Z 5 Z 4 › Z 2 Z 4 Z 3 . (29) After orthogonalization (29) we obtain the P-risk model:

P = p 2 p 4  p1 p3  q1 p 2 p3q4 p5  p1q2q3 p 4 p5  p1 p 2 p3 p 4. (30) The minimal cut sets of failures. Actually, it does not matter whether we write down the L-function for success or failure, as the probability of failure q=1–p, where p is the probability of success. The failure risk analysis is quite often important. Then it is more convenient instead of (28) to write down the L-function of system failure as the minimal cut sets of failures (ɆɋɈ) of elements [9, 16] Y = Z1 Z 2 › Z 3 Z 4 › Z1 Z 5 Z 3 › Z 2 Z 5 Z 4 (31) Then we have to make the orthogonalization of this function and to write down the P-polynomial of risk.

1.9.2.

Associative LP-risk Models

The scenario of the system state failure can be associative [7]. For example, the failure causes one IE, any two or all of them from Z1, Z2,…,

Chapter One

40

Zn. The L-failure risk model is a subset of PDNF. Here we also need the orthogonalization of the L-function in order to obtain the P-risk function. For example, the L-risk function of the associative model failure: (32) Y = Z1 › Z 2›... › Z j›... › Z n , where Z1,…, Zn are logical variables for the parameters of the state. The logical orthogonal function risk of the associative model failure risk:

Y = Z1 › Z 2 Z1 › Z 3 Z 2 Z1 › ....

(33)

From (33) we get the P-risk function of the associative model failure: P (Y ) P1  P2 (1  P1 )  P3 (1  P1 )(1  P2 )  ..., (34) where Pj is the probability of event Zj causing the failure of Y.

1.9.3.

Tabular Assignment of LP-risk Models

Let us use the “bridge” example in order to describe the construction of the LP-risk model in the tabular mode [7, 8]. There are four ways of successful operation: S1, S2, S3, S4. At the same time: S1 assign events Z1, Z3; S2 assign events Z2, Z4; S3 assign events Z1, Z4, Z5; S4 assign events Z2, Z3, Z5. Let us introduce the connections of events S1, S2, S3, S4 and initiating events Z1, Z2, Z3, Z4, Z5 as a table of connections (Table 5: 1 - presence of connection, 0 - lack of connection) and write out the L-function for derivative events S1, S2, S3, S4:

­ S1 °S ° 2 ® ° S3 °¯ S 4

Z1 Z 3 ; Z2Z4 ; Z1Z 4 Z 5 ;

(35)

Z 2 Z 3Z5.

The model of successful operation of the bridge can also be represented as the functional integrity scheme (Fig. 6). The disjunctive normal form of the logical function of the bridge’s successful operation can be written down in the following way:

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41

Y = S1 › S 2 › S 3 › S 4 .

(36)

Finally we obtain the same L-function of the successful system performance (30). Certain L-variables are included in the derivatives of Levents several times. For example, Z1 is included in S1 and S3, while Z5 is included in S3 and S4, etc. This leads to the L-function for final event Y becoming the L-function with repeated elements. In order to make a transition from the L-risk function to the P- risk function, we have to convert Y to the logical iteration-free orthogonal form. Table 5. The tabular setting of the logical model of “the bridge” The state Z1 1 0 1 0

S1 S2 S3 S4

Initiating events Z2 Z3 0 2 1 0 0 0 1 1

Y

S1

6

S2

7

Z4 0 1 1 0

Z5 0 0 1 1

10 S3 8

S4

9

1

2

3

4

5

Z1

Z2

Z3

Z4

Z5

Fig. 6. The functional integrity scheme for the bridge

42

Chapter One

1.9.4. Development of Complex LP-risk Models A complex LP-model is the one including repeated events. The construction of such models is discussed in [7, 9]. Structurally complex systems include several subsystems which can have several common or repeated events. In complex LP-risk models separate scenarios and LPmodels are combined with the operations OR, AND, NOT. LP-risk models with repeated events are especially interesting, because economic processes are interconnected. An LP-risk model can be so complex that L- and P-risk functions do not fit in the computer memory or the summons of the P-function contain a large number of multipliers and, thus, risk assessment becomes inaccurate. In this case the model decomposition should be used and the initiating events must be folded in nodes OR and AND. In different scenarios for the same events different terms could be used, and it is not easy to find repeated elements among dozens and hundreds of events. The following rules of building complex LP-risk models might be of some use: 1) the search for external and internal initiating events in the scenarios; 2) the folding of initiating events, if there appears a problem of storing the L-risk model in computer memory; 3) the decomposition of a complex LP-risk model into a few simple ones, if in the P-model the summons have a lot of multipliers > 20 and the calculations lose their accuracy; 4) the combination of the results of simple models according to their L-connections. If the subsystems of a complex system have no common events, then the failure of each one can be treated separately, and the failure of the whole system could be obtained by the combination of events for subsystems by L-operations OR, AND, NOT. These are the examples of external IE: 1) for a company: the events in the economy of the country and world economy; 2) for an operating department of a plant: events in the central offices, planning, financial and procurement departments; 3) for a city: natural disasters, flu epidemics. In complex LP-risk models logical and probabilistic risk models may not always fit into RAM. In the software complex ACM-2001 these models should have no more than 600 summonses; then for building the

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43

logical and the probabilistic failure risk models we have to simplify the setting and notation. Therefore, we propose to fold IE in nodes OR, AND. The LP-risk and efficiency model with several aims. The construction of the system of LP-risk models is performed in the following order: the scenario is formulated, the structural model is built, the L-model is written down, and the P-risk model (polynomial) is obtained. An LP-risk model can be made up for the random risk scenario. The scenario is developed from top to bottom: at first the event is determined, then - the events causing it, etc. At least two links suit each node (derivative event). Only one link with L-connection OR, AND, NOT emerges from each node. At the lowest level the events are given the name “initiating” and their probabilities are defined. The rest of the events are called derivative and their probabilities are calculated. If a complex system has two outputs it is possible to analyze the following complex events (logical models) [9, 16]: 1) The L-function of the realization of at least one criterion (Y1 OR Y2); 2) The L-function of the non-realization of all criteria (NOT Y1 AND NOT Y2); 3) The L-function of the realization of both criteria (Y1 AND Y2); 4) The L-function of the realization of only the first criterion (Y1 AND NOT Y2); 5) The L-function of the realization of only the second criterion (NOT Y1 AND Y2). Different risk scenarios can be logically combined into one P-model, using operations OR and AND. If different models or aims have different efficiency parameters E1, E2, …Em of the same essence and dimension, then the efficiency of the complex model is calculated from the expression E=P1E1+P2E2+…+ PmEm , (37) where P1, P2,…,Pm are the failure risks (probabilities) of separate models. If different models or aims have efficiency parameters E1,…,Em of different nature and dimension, then the efficiency of the complex model must be considered as vector E=(E1, E2,…,Em).

1.9.5. Development of Invalidity LP-models of Systems Assessment of the quality of systems, services and goods is a statutory requirement of WTO. It is quite difficult to build invalid LP-models for assessing the quality of system performance. In the problem of LP-risk

44

Chapter One

management of the invalidity of systems the following aspects [7, 8] are considered: 1) engineering-economic: the search for the states and initiating parameters causing invalidity; 2) methodological: the definition of the notion of invalidity as an event by analogy with the event “failure” and “operation failure”; 3) logical: the definition of the invalidity of events, L-variables and the shortest paths of validity and invalidity; 4) computational: the transition from the L-risk model to the P-risk model of invalidity, which often has high computational complexity. The development of the invalidity scenario is a creative process. Only a specialist knowing the system performance can define the full number of invalid states. LP-risk models of SES invalidity have repeated events. Repeated events is the reason for the large number of system states combinations. I. Ryabinin was the first to study a complex LP-model with repeated events. It was the model of the reliability of a submarine’s electrical supply [9]. The LP-risk model of system invalidity is built from top to bottom. The upper section of the structural model of a system is an event of system invalidity as a disjunction of the derivatives of events Y1, Y2, Y3, Y4. The Lrisk model of system invalidity Y is a logical combination of L-models: Y = Y1 › Y2 › Y3 › Y4 . (38) The L-model of invalidity is reduced to its orthogonal form. After that the P-model is obtained which is used for quantitative calculation of invalidity risk and of IE contributions to the risk of system invalidity Y. Land P-models for Y1, Y2, Y3, Y4 are built and analyzed simultaneously. LP-models of invalidity risk use the shortest paths of successful operation (validity) or the shortest paths of invalidity emergence. No minimal cut sets of failures are used. When describing invalidity the invalidity of system states (derivative events) and initiating events is considered.

1.10. Risk LP-analysis of Socioeconomic System States The quantitative LP-analysis of system risk is performed algorithmically by making calculations on the computer. It is distinguished by simplicity and transparency.

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In the LP-efficiency class the statistical data from a set of system states are considered, for example, daily returns on equities Z1, Z2,…,Zn from the investments’ portfolio, according to the data from the stock exchange. The events of the occurrence of the states are considered. A statistical tabular database (DB) is transformed into a tabular Knowledge Base (KB) by introducing events-grades for the returns on equities and portfolio. The efficiency parameter (portfolio yield) Y is calculated depending on the returns on equities and capital shares x1, x2,…,xn, invested in equities for each portfolio state. The distribution histogram is built for efficiency parameter Y. The probabilities of states Yi occurrence are calculated according to the frequencies of their occurrence. Frequency analysis of risk and efficiency consists in the quantitative assessment of the contributions of grades of parameters Z1, Z2,…,Zn, describing the state, to the risk and efficiency in the tail of the efficiency parameter distribution. The frequencies P2jr of events-grades for the left “tail” L, right tail R and center C are calculated. For example, for the left “tail” of the distribution of the efficiency parameter P2jr ad = Njr / Nad , j=1,2,…,n; r=1,2,…,Nj , where Nad, Njr — the numbers of all events and events-grades in the tail. The calculation of contributions of events-grades into the left “tail” L, the right “tail” R and the center C is much simpler and more efficient than the use of the “copulas” apparatus, for which analytical distributions are selected. In LP-modeling and LP-classification classes the quantitative analysis of system risk is conducted by the significance and contributions of IE to the probability of the final and derivative events. Structural significance takes into account the number of different paths with an i-event, leading to the final event; using the P-risk function we can determine: 'Pi = Py | Pi=1  Py | Pi= 0 , i = 1,2 ,...,n, (39) where Py is the probability of the final event, Pi is the IE probability, and the values of probabilities of other IE P1=P2=….=Pn=0.5. The probabilistic significance of an i-event takes into account its place in the structure and its probability. Probabilistic significance and contributions are calculated with real values of IE probabilities. The contributions of events to the minus and to the plus in the final event probability are defined by giving values 0 and 1 to the probability of the value in the P-risk function. The significance of i-event:

46

Chapter One

'Pi = Py | Pi=1 Py |Pi=0 , i = 1,2 ,...,n,

(40)

The contribution of i-event to the minus:

' Pi  = Py | Pi  Py | Pi=0 , i = 1,2 ,...,n,

(41)

The contribution of i-event to the plus:

'Pi+ = Py | Pi  Py | Pi=1 , i = 1,2 ,...,n.

(42)

The simplicity and transparency of risk analysis is one of the main advantages of LP-risk models for SES economic safety management.

1.11. LP-forecasting of Risk in States Space The problem of forecasting is one of the most complex ones in science and economy. LP-risk models provide us with new forecasting opportunities, namely, forecasting in the space of system states. In the LP-modeling class the risk of new states or objects is predicted (assessed) by the insertion of the values of IE probabilities. In the LP-classification class (Fig. 3) the problem of LP-risk models identification by statistical data is solved, for example, the data about bank loans. The number of bank loans can reach several hundred thousands. The identification task consists in finding the probabilities of initiating events-grades, using limited statistical data, for example 1000 loans, with the known assessment of their success. The LP-model of the loan risk of a bank, built in this way, is used for predicting (assessing) the risk of new loans which were absent from the statistical data, i.e. the risk of new loans is predicted in the space of states by actual loan parameters. In the “Efficiency” class the situation is different and more difficult to predict. The risk model is built by statistical data (dynamic series) as the distribution of the efficiency parameter (shares portfolio yield, company profits, public opinion polls results, etc.) (Fig. 4). Let us describe in more detail the forecasting procedure for risk models of the LP-efficiency class. For the purposes of forecasting system risk a transition is made from risk models of the “LP-efficiency” class to risk models of the “LPclassification” class. In the “LP-classification” class (Fig. 3) the efficiency parameter Y takes two values: 1 – a good state and 0 – a bad state. The risk of system states classification is determined by the condition: Risk=P (P > Pad ), where Pad – admissible risk.

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In the scheme of risk for the “LP-efficiency” class (Fig. 4) the distribution for the efficiency parameter Y is used. Risk is defined by the condition: Risk=P(Y < Yad), where Yad – admissible risk. The model of the “LP-classification” class (Fig. 3) has greater potential for risk analysis compared to the risk models of the “LP-efficiency” class (Fig. 4). Let us deal with the corresponding transformation. Let the admissible value of efficiency parameter Yad be chosen. Let efficiency parameter Y (Fig. 4), as a random variable, have two values: 0 – a good one and 1 – a good one. The system state is bad Yi < Yad and the system state is good Yi > Yad. Now we will calculate the admissible risk of the failure of process Pad=Nad / N, where Nad is the number of states which got into the tail according to condition Yi > Yad. It should be noted that, because of the sense of the problem, we might study the tail in the distribution of the efficiency parameter both from the right side and from the left side. Let us now use the equations system (18) – (19) for the definitions of states failure risk. Suppose the system identification problem has been solved (19), probabilities Pjr, j = 1, 2,…,n; r =1, 2,…,N.j have been defined and the risks of all states have been calculated. Condition Pi > Pad divides the system states into good ones and bad ones according to the value of states risk (Fig.3). Example. System risk can be predicted on the basis of the analysis of contributions of events-grades of initiating processes (for example, the price of the shares from the portfolio) into the tail of the distribution of the system efficiency parameter. In frequency analysis the contributions are determined directly by statistical data by calculating the ratio of dangerous states Njr, containing gradation r of parameter j, and all dangerous states Nad. Let us assign only two values (0 – bad and 1 – good) to efficiency parameter Y (Fig. 3) as a random value. In this way the risk model of the “LP-efficiency” class is transformed into the risk model of the “LPclassification” class. The probabilities of events-grades Pjr are determined by solving the identification problem by statistical data. After that, probabilistic analysis is conducted for assessing the risk of system states absent from statistical data (forecasting in the states space). Indeed, the total number of system states is great (9) and only some of these states are present in statistics. In order to calculate the risk of system states which have not occurred yet we have to insert probabilities Pjr, corresponding to the events-grades of initiating processes, into (19). This is what makes LPrisk analysis different from frequency risk analysis, which is conducted only for system states which have actually occurred.

Chapter One

48

1.12. Risk LP-management of Socioeconomic Systems LP-risk management of system state and development is performed with the help of LP-risk models and calculations on the computer. LP-management of system state risk (operating management) is performed by qualitative analysis of the significance and contributions of IE, from the LP-risk model of SES state, to the final risk. The following types of management are possible: 1. The reduction of risk (probabilities) of the most significant IE by investing resources and improving personnel skills; 2. The change of the system’s structure and the model of economic safety risk; 3. The introduction of supporting units into the system’s structure and the model of economic safety risk; 4. The alteration of SES operation by excluding redundant elements and connections which increase system risk. The increase of the number of authorities and officials taking decisions leads to risk growth due to bribery, corruption and incompetent decisions. The risks in the system are added logically. The more elements there are in the system, the greater is the risk. Works [7, 8] deal with the problems of LP-risk management in LP-models of different classes in more detail. LP-management of system development risk (strategic management) is performed according to the scheme of complex object management. It consists in managing the movement along the programmed trajectory and making corrections in case there are some deviations from it (Fig. 7). The development program includes possible troubles and resources (finances, qualified staff) for corrections to be made. The values of parameters at the development stages are calculated in the program.

Wj

Py

Py n

Py1

B

Uj

Py j

Py 2

Cj

D

j

A

1

Fig. 7. System evolution management

2

j

Stage N

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49

Key to Fig. 7: Pyj – the probability of successful development; Uj – management, including structural changes; Wj – corrections, including structural changes; j=1, 2,…,n – stages of development. The system is transferred from initial state A into the final state B along the trajectory A– B during several stages. The program calculates the values of parameters Pj, Uj, Wj and includes expenses (resources) for management and corrections Uj, Wj at development stages N, ɚs well as the possible losses of time and money in case of their lack [7]. The L-risk model of system development failure at all stages:

Y = Y1 › Y2 › ... › Yn ,

(43)

Y1 , Y2 ,..., Yn are the logical functions of system development failure (risk) at the stages. The P-model risk of system development failure: R^Y = 0`= R1 + R2 (1  R1 ) + R3 (1  R1 ) (1  R2 ) + .... , (44)

where R1, R2,….,Rn are the risks (probabilities) of the failure of events. Thus, at each stage of development and for the whole process of development the problems of analysis and SES economic safety management are solved.

1.13. Dynamism of LP-risk Models The dynamism of LP-risk models of socioeconomic systems is achieved by the correction of IE probabilities in the following cases: x the emergence of new statistical data concerning system states; x the emergence of new signal events in economy, politics, law and innovations; x the improvement of employees’ skills; x the change of the situation in the world market; x reforms in education, science and economy. In case there are no statistical data, the synthesis of the probabilities of initiating events is performed on the basis of non-numerical, inaccurate and incomplete expert information using N. V. Hovanov’s method of randomized indexes. In certain cases LP-risk models can be built as dynamic ones, inserting time in the model as the parameter-date of, say, loans receipt.

Chapter One

50

1.14. Synthesis of Events Probabilities In LP-models of risk management of SES state and development, when there are no other data, the probabilities of events are assessed by nonnumerical, inaccurate and incomplete (NII) expert information. The synthesis of IE probabilities is conducted on the basis of the aggregate indexes technique by NII-information [14]. An expert cannot give the exact assessment of the probability of one event. He will do it in a more precise and objective manner if he assesses 2 to 4 alternative hypotheses and takes into account their weights (an expert is “rocked”). Hypotheses A1, A2,…,Am are formulated. Weighting factors of hypotheses w1, w2,…,wm are reckoned discretely at a pitch of h=1/n, where n is the number of grades of the weights of hypotheses (for example n=50 ). In other words, the weights take values from the set ^ 0, 1 / n, 2 / n,..., (n  1) / n, 1 `. (45) A set of all possible vectors of weighting factors:

W (m,n) = N1 N 2 ...N m

(46)

where N1, N2,…, Nm – the number of grades in weighting factors. Expert information about weighting factors is defined as ordinal order information and interval information. Ordinal order expert information: OI = wi > w j , wr = ws ; i, j,r, s  ^1,...,m` . (47)

^

`

Interval expert information:

II = ^ ai d wi d bi ; i  ^1,...,m``.

(48)

Pooled expert information is called non-numerical, inaccurate and incomplete. Naturally, the following condition also holds true: w1 + w2 + ... + wm = 1 . (49) Conditions (47) – (49) define the tolerance region of weighting factors w1, w2,…,wm. Mathematical expectations of randomized weighting factors are used as numerical assessments of weighting factors. The accuracy of these assessments is measured by standard deviations. The calculations are repeated for at least two experts. The table of assessments of weighting factors of hypotheses from all experts is made up. The aggregate assessment of weighting factors w1*, w2*,…,wm* of hypotheses A1, A2,…,Am is calculated using the data from the table and

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now the weights of the experts themselves, defined by the super-expert by the above technique. The hypothesis with the highest assessment of the aggregate weighting factor is selected. Analysis of IEs probabilities is performed using the known risk of the derivative event Py, which they are part of. It allows one to manage risk, changing IEs probabilities by investing resources. The problem is solved according to the scheme which is close to the events probabilities synthesis scheme. Initiating events w1*, w2*,…,wm* have weighting factors w1, w2,…,wm., which are reckoned discretely at a pitch of h=1/n, where n is the number of weight grades in IE. NII-expert information by IEs weights, which are part of the derivative event, is defined as ordinal order information (47), interval information (48) and balance (49). These conditions define the tolerance region of weighting factors w1, w2,…,wm. Mathematical expectations of randomized weighting factors are used as numerical assessments of weighting factors. The accuracy of these assessments is measured by standard deviation. The calculations are repeated for at least two experts. A summary table of the assessments of IE weighting coefficients from all experts is made up. The aggregate assessment of weighting factors w1*, w2*,…,wm* of initiating events w1*, w2*,…,wm* is calculated using the data from the table and at this point the weights of the experts themselves are defined by the super-expert. The probabilities of IE are:

P1 = Py w1 ; P2 = Py w2 ; ...; Pm = Py wm .

(50)

Formula (50) is employed if IE are connected by the logical operation OR and the assessment of IE probabilities does not exceed 0.02. In this case the results of arithmetic and logical addition of IE probabilities are virtually the same. If the assessment of IE probabilities exceeds 0.02, then the obtained probabilities IE P1, P2,…,Pm must be corrected according to the formula: P1 = K1 P1 ; P2 = K1 P2 ; Pm = K1 Pm , (51) where K1 is the correction factor, which is the ratio of the logical sum of the IE event probability to the arithmetic sum. The allocation of resources for components A1, A2,…,A.m, of the system is conducted, if one knows the value of resource Qres for the system which they are part of. It allows us to manage a system’s development. Resource allocation is reduced to finding the share of ti, i=1,2,…,m of components A1, A2,…,Am in the volume of the resource. Shares ti, i=1,2,…,m of components A1, A2,…,Am are assessed according to the

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scheme of IE probabilities analysis. The resources allocated for the components are: Q1 = t1Qres ; Q2 = t 2 Qres ; ...; Qm = t m Qres . (52)

1.15. Regulation and Management in Economics Regulation. In economics, the term “regulation” is used in the titles of dissertations and economic research (e.g., regulation of operational risk in bank). The regulation refers to the operating system and it looks as follows. If some output indicators deviate from requirements, then we reduce the deviation of output indicators by the regulation (change) of input parameters. The specialist, as a rule, knows if each output indicator decreases or increases with the increase or decrease of each input indicator, but the specialist does not know quantitative values. The correlation between indicators is inaccurate because the distribution of indicators is not normal due to internal active management and external impact of the global market. Regression dependence is also inaccurate because it is impossible to consider all factors and choose the correct type of dependency. At the same time it is necessary to make decisions by real-time monitoring of the results for the concrete state of the system, allocating resources to improve its quality. The manager makes a decision without the use of mathematical models. Therefore, the regulation of the state of the system without a mathematical model is rightly called control “by concepts.” Management. Unlike mathematics and mechanics, we do not deal with automatic control in economics, instead we deal with automated management performed by the decision-making manager. Norbert Wiener, one of the founders of cybernetics, wrote that the management model in economy and society cannot be based on differential equations and regression, but should be based on logic, sets and probabilities. To manage the state of the economic system it is necessary to formulate the criteria for management and build a mathematical model. The model of the system’s state is needed to assess its quality, to analyze its condition, and to manage and forecast the system’s states. The efficiency and risk of the system are transparent and clearly related criteria. The risk of the system’s state is correctly calculated in the function of initiating events. In the present work, control of the socioeconomic system is considered as the following steps: x the construction of invalidity,

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x analysis of the system’s invalidity model by the contributions of parameters which influence the system’s risk, x decision about reducing the risk of influencing parameters, x the allocation of resources to reduce the risk of influencing eventsparameters. The invalidity of the LP-model of the system can be built by the parameters of one system state.

1.16. Objective and Subjective Invalidity The central concept of top-economics is the invalidity of socioeconomic systems. Let us give a philosophical explanation of this concept by analogy with the concept of safety in engineering [9]. Invalidity is an event which causes a system to perform a given task, but with quality loss. In practice, there can be difficulties in the assessment of invalidity which one person represents as the deviation from the specified requirements, and the other person – 0. Why does the same fact lead people to have different opinions about the validity and invalidity of a system? What is objective and what is subjective? Every system (object) can be described in various ways. One way is to describe the preparation of the final set of requirements to be satisfied by an object. If an object satisfies all the requirements, it is valid. Drawing up a set of requirements for the system we associate with the activities of some people. Therefore, it is a subjective act, depending on the completeness of the knowledge about a system, experience and other facts. Errors are possible in the appointment of certain requirements and the omissions of others. Moreover, these requirements can change at the will of developers, i.e. they are dynamic. Despite the completeness of a system’s requirements and the subjective nature of establishing them, at any time a certain set of requirements (standards) should be allocated and fixed, in relation to which requirements it is possible to objectively assume the validity or invalidity of a system. This is the dialectic of subjective and objective in the assessment of invalidity: we set requirements for a system subjectively and we consider its status with respect to these requirements objectively.

1.17. Connection between SES and Environment In top-economics the informational connection of a socioeconomic system with environment is used. Informational connection is provided by

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signal events and used for correction of a SES risk model in order to increase the accuracy of estimation and analysis of invalidity and danger of a system’s state. A decision-maker manages SES by allocation of resources to reduce a system’s invalidity, and proceeds from new estimation of invalidity and the contribution of initiating events to invalidity. The informational connection of SES with environment is not free of charge. Systems of monitoring signal events are organized and the technology of correction and analysis of the LP model of a system's invalidity is developed, including the frequency of the model's correction and allocation of resources. Signal information from signal events has quantum nature, which is usual in environment, and is an important part of management in economics. For every socioeconomic system there exists a finite set of signal quantum information sources. The energy (significance) of a quantum is different, like the energy of a light quantum depends on the frequency of the light wave oscillation. Most effectively, signal information is used in business due to the possibilities of flexible operative management, but in a State system, as a rule, resources are allocated a year or even five years before. Informational connection between the environment and the socioeconomic system on the basis of signal information, realized with LP risk models, is one more principle of management of economic systems together with Li Keqiang’s principle of the equivalence of technological innovations and innovations in State administration, and the Nobels’ principle of social fairness.

1.18. Unforgotten Knowledge This section deals with additions and comments on risk management technologies, as well as with logical addition of probabilities and arithmetic addition of weights. Logical addition (L-addition) of failure events Z1, Z2,…,Zn: Y = Z1 › Z 2 › ... › Z j › ... › Z11. (53) is formulated as follows: a failure occurs, if any IE, any two IEs, or all of them happen. The P-model is written down after the orthogonalization of the L-model: P p1  p 2q1  p3q1q2  ..., (54)

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where p1, p2,… are the probabilities of events-parameters Z1, Z2,…; q=1p. Arithmetic addition (Ⱥ-addition) of the weights of events: P P1  P2  P3  ...  Pn , (55) where P1, P2,…,Pj,…,Pn are the weights of events Z1, Z2,…, Zj,…, Zn. The LP-model provides the value of P in the interval [0, 1] at any values of probabilities IE 0 < Pj < 1; j=1,2,…,n. The probability of the final event P with two or more IE depends on IE probabilities in an S-like manner. The slope of S-dependence increases with the growth of the number of IE. The probability of the final event and its saturation during L-addition depends on the number of IE and their probabilities. The weight of the final event P during the logical addition of the weights of initial events also depends on their number and on probabilities. At the large values of weights Pj, j=1,2,…,n events and their large number, the weight of the final event becomes absurdly big (P>1). Arithmetic and logical sums are close to each other only when the values of probabilities of IE are small and their number is small too. Therefore the techniques, based on Ⱥ-addition (the only kind of addition used in economics), have a satisfactory accuracy with a number of parameters n =3 - 5 and their small weights Pj §0.01, j=1,…,n [7, 8]. Unforgotten knowledge. Recollect that “unforgotten knowledge” is the knowledge used in management technologies with LP-models. A lot of economists know nothing about this knowledge. Condition 1. Boolean statements have become the foundation of mathematical logic. They were developed into events in engineering and became the basis of the reliability theory. Boolean statements found practically no use in economics. Due to globalization and the emergence of more complex processes in economics it would be useful to recollect and develop Boolean statements in order to increase the efficiency of the economy. Condition 2. It is time we returned to the basics – logic and sets - in order to solve difficult problems. At the end of the 19th Century, mathematics witnessed the development of non-constructive set-theoretic trends (see the works of K. Weierstrass, R. Dedekind and G. Cantor) [29]. The theory of sets was just appearing. It was supposed to become a basis of problem setting in mathematics. According to G. Cantor, “the essence of mathematics is in its freedom”. This theory allowed a certain arbitrariness in the process of introducing “sets”, which were later treated as finished “objects”. However, in the early 20th Century antinomies were discovered – the

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discrepancies, which showed that “objects” and “sets” cannot be combined arbitrarily and the notion of “infinity” can be used. Attempts to overcome the difficulties were made in the process of transforming the theory into a kind of axiomatic science like geometry. It was done in such a way as to make everything necessary for the substantiation of mathematics to be based on axioms and to get rid of the known antinomies. E. Zermelo proposed such a system of axioms. However, there were no guarantees that there would not be any discrepancies. A limited number of elements is used in the application of risk management technologies in SES. A lot of problems can be successfully solved on the basis of sets theory and logic. Condition 3. The outstanding scientists Norbert Wiener and John von Neumann believed that mathematical methods used for managing complex socioeconomic systems must be based on combinatorics, logic and sets. Condition 4. Rudolf Kalman, the author of the Kalman filter, stated that it might surprise some mathematicians that the problem “data Æ the model explaining the data” should be treated as the main one for any branch of science. Condition 5. W. Occam believed that there is no need sophisticate the model without any valid reason. Simple explanations are also likely to be correct. Some scientists think that sets and LP-models are the simplest and most transparent elements of mathematics. Condition 6. Economic safety should be managed according to universal rules, understood similarly by everyone, and not on the basis of various notions that different subjects have.

1.19. Concepts and Principles of Safety Management of SES The following concepts, principles and theorems are actual in developing the safety management systems of SES: 1) The principle of management by the risk criterion with an estimation of possible losses. 2) The concept of social justice in society by the Nobels’ principle. In fact, according to this principle, a significant part of the company’s profits should be spent on workers: the Nobels paid decent wages, built homes, kindergartens and schools, provided a free medical service to their employees, retrained them, and invested in science and innovation.

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3) The concept of the Chinese leadership (Li Keqiang) consists in the fact that technological innovations and innovations in management, including State management, are treated equally. 4) The principle of managing the development of a system as a complex object moving along the program trajectory with corrections in case of deviations from it. 5) The principle of management by signal events with correction of probabilities of initiating events of the LP-risk models of SES. 6) The postulate. Socioeconomic problems are not solved without scientists and public opinion. 7) The concept of American lawyers: everyone can make fraudulent actions in a difficult life situation, especially if this fraud can be concealed, at least, temporarily. 8) The concept of Russian lawyers: commercial banks and companies are capable of fraudulent actions because they want maximum profits if they are not controlled. The activities of banks and companies are not transparent, nor are the techniques of the assessment of ratings, and that can also be explained by the allpermeating desire to deceive and swindle. Principles are realized in mathematical models of socioeconomic safety management, concepts are realized in technologies of safety management of socioeconomic systems. The postulate is proved by modeling and experience.

CHAPTER TWO EXAMPLES OF LOGICAL AND PROBABILISTIC MANAGEMENT OF SOCIOECONOMIC SAFETY

In science examples are as instructive as theory I. Newton

These examples of logical probabilistic management of economic safety cannot be said to provide a comprehensive analysis of the problems. They are aimed at illustrating the possibility of managing the safety of the economic problems under study. The assessment of the Russian economic health criteria and the standard of living of our population is not very high. Therefore, we have to study the problems of socioeconomic safety management. In order to manage the economic safety of the SES and the country we have to build LP-risk models of their condition. After that, these LP-risk models are used for the analysis, forecasting and management of economic safety. We are going to describe examples of LP-management of SES economic safety from groups SES-1, SES-2 and SES-3 – the objects controlled by top-economics: SES-1 are of top priority for the State, SES-2 are complex ones, for the State and the regions, SES-3 are local ones, for companies and firms. For each SES under consideration we have to know which group it belongs to and whether it is aimed at reducing financial losses or at increasing revenues.

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2.1. Logical and Probabilistic Risk Management of Economic State of Russia However complex a problem can be, it will become more complex if we look at it from the wrong angle. P. Anderson

The SES under study belongs to the group of complex SES-2. SES management is aimed at increasing the economic safety of a country. The safety of a country depends not only on military, technical, technological, energy, ecological and information safety [1], but also on economic safety – sustainable development of SES, systems of counteraction to corruption and drug addiction in a country, etc. In this respect, we have adopted the principle of the Chinese leader Li Keqiang as the basis, according to which technological innovations are viewed as equal to innovations in management, including State management. We deal with the LP-risk models of the system “Logical probabilistic management of the risk of economic state and evolution of Russia” on the basis of the Nobels’ concept of social justice [30]. Three generations of the Nobels worked in Russia in the 19th and early 20th centuries. Their business concept consisted in spending a significant share of their profits to support their employees: to pay them decent salaries, to improve their skills by training programmes, to build houses, kindergartens and schools, to provide a free medical service, to invest in science and innovations.

2.1.1. LP-risk Model of Economic State The core of the complex SES “Management of the economic safety of Russia” consists of a combination of the complex SES and two LP-risk models [12]: 1. The LP-risk model of birth rate. 2. The LP-risk model of housing construction. In the combined scenario 33 initiating and derivative events are connected by logical links OR, AND, NOT. The LP-risk model of the economic state of Russia can logically include other models and scenarios, for example, the LP-models of counteraction to bribery and corruption, counteraction to drug abuse, the innovations system management, etc. The structural model. The LP-risk model of the economic state in Russia Y33 is built by the logical addition of the birth rate LP-risk model Y32 and the housing construction LP-risk model Y31 (Fig. 8). In this figure

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one can see the names of initiating and derivative events, their identifiers and types of L-connections: the link with the arrow means the OR connection, the link with a point means the AND connection. The initiating events of the risk scenario “Housing construction conditions” are the following ones: Y1 – increase of workplaces number, Y2 – top quality education, Y3 – competition growth, Y4 – tendering process, Y5 – the purchase of futures, Y6 – the search for suppliers, Y7 – social programs, Y8 – mortgage rates decrease, Y9 – economic stability in the country. The initiating events of the risk scenario “Birth rate situation” are the following ones: Y10 – legal protection of mothers, Y11 – legal protection of families, Y12 – provision of housing, Y13 – assistance to needy families, Y14 – the “Health” Program, Y15 – the growth of employees’ salaries, Y16 – State support, Y17 – the construction of new kindergartens, Y9 – economic stability in the country, Y18 – quality improvement, Y19 – free medical service, Y20 – leisure, Y21 – constant income of a family. The derivative events of the risk scenario “Economic health of Russia” are the following ones: Y22 – decrease of building materials prices, Y23 – the growth of the population’s income, Y24 – realty prices decrease, Y25 – housing purchase availability, Y26 – legal coverage, Y27 – implementation of social programs, Y28 – pre-school education guarantees, Y29 – medical service improvement,

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Y30 – strengthening of family ties, Y31 – realty demand growth, Y32 – birth rate increase in Russia, Y33 – successful state. It should be noted that, in the risk scenarios of the three complex SES under study, the events which are used refer to economy, politics and law, i.e. the solution of the problems depends on various ministries and government bodies. In case there are no statistical data, the probabilities of initiating events Y1, …,Y21 are assessed by expert information [14]. Let us introduce the notation: Y33, Y32, Y31 – logical variables of targets of the combined LP-risk model. Derivative events: Yd(›, Yd1, Yd2,…) – the connection of Yd1, Yd2,… by L-link OR; Yd(š; Yd1, Yd2,… ) – the connection of Yd1, Yd2,… by L-link AND. The L-risk model of the economic health of Russia can be written down as sequences:

Y33 (š;Y32 ,Y31 ); Y31 (š;Y23 ,Y24 ,Y25 ); Y32 (š;Y26 ,Y27 ,Y28 ,Y29 ,Y30 ); Y22 (› ;Y5 ,Y6 ); Y23 (› ;Y1 ,Y2 ); Y26 (› ;Y10 ,Y11 ). Y24 (› ;Y3 ,Y4 ,Y22 ); Y25 (› ;Y7 ,Y8 ,Y9 ); Y27 (› ;Y12 ,Y13 ,Y14 ); Y28 (› ;Y15 ,Y16 ,Y17 ); Y29 (› ;Y9 ,Y18 ,Y19 ); Y30 (› ;Y20 ,Y21 ). (56) The logical risk model of the economic state of a country. Calculations in LP-risk management have high computational complexity. The software ACM–2001 was used for LP-management of the risk of the state and the development of socioeconomic systems, while ASPID–3W and Expa were used for the synthesis of the probabilities of initiating events.

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Fig. 8. The structural risk model of the current situation in Russia

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The software ACM—2001 automatically built the logical risk model on the basis of the structural risk model (Fig. 8). In machine notation the L-risk state model for the derivative event Y32 “Birth rate state” in the disjunctive normal form looks as follows (the figures – the numbers of logical variables; “.” – logical multiplication, “+” – logical addition): Y32 = 9.11.14.17.21 + 9.10.14.17.21 + 9.11.13.17.21 + 9.10.13.17.21 + 9.11.12.17.21 + 9.10.12.17.21 + 9.11.14.16.21 + 9.10.14.16.21+ 9.11.13.16.21 + 9.10.13.16.21 + 9.11.12.16.21 + 9.10.12.16.21 + 9.11.14.15.21 + 9.10.14.15.21 + 9.11.13.15.21 + 9.10.13.15.21 + 9.11.12.15.21 + 9.10.12.15.21 + 11.14.17.19.21 + 10.14.17.19.21 + 11.13.17.19.21 + 10.13.17.19.21 + 11.12.17.19.21 + 10.12.17.19.21 + 11.14.16.19.21 + 10.14.16.19.21 + 11.13.16.19.21 + 10.13.16.19.21 + 11.12.16.19.21 + 10.12.16.19.21 + 11.14.15.19.21 + 10.14.15.19.21 + 11.13.15.19.21 + 10.13.15.19.21 + 11.12.15.19.21 + 10.12.15.19.21 + 11.14.17.18.21 + 10.14.17.18.21 + 11.13.17.18.21 + 10.13.17.18.21 + 11.12.17.18.21 + 10.12.17.18.21 + 11.14.16.18.21 + 10.14.16.18.21 + 11.13.16.18.21 + 10.13.16.18.21 + 11.12.16.18.21 + 10.12.16.18.21 + 11.14.15.18.21 + 10.14.15.18.21 + 11.13.15.18.21 + 10.13.15.18.21 + 11.12.15.18.21 + 10.12.15.18.21 + 9.11.14.17.20 + 9.10.14.17.20 + 9.11.13.17.20 + 9.10.13.17.20 + 9.11.12.17.20 + 9.10.12.17.20 + 9.11.14.16.20 + 9.10.14.16.20 + 9.11.13.16.20 + 9.10.13.16.20 + 9.11.12.16.20 + 9.10.12.16.20 + 9.11.14.15.20 + 9.10.14.15.20 + 9.11.13.15.20 + 9.10.13.15.20 + 9.11.12.15.20+ 9.10.12.15.20 + 11.14.17.19.20 + 10.14.17.19.20 + 11.13.17.19.20 + 10.13.17.19.20 + 11.12.17.19.20 + 10.12.17.19.20 + 11.14.16.19.20 + 10.14.16.19.20 + 11.13.16.19.20 + 10.13.16.19.20 + 11.12.16.19.20 + 10.12.16.19.20 + 11.14.15.19.20 + 10.14.15.19.20 + 11.13.15.19.20 + 10.13.15.19.20 + 11.12.15.19.20 + 10.12.15.19.20 + 11.14.17.18.20 + 10.14.17.18.20 + 11.13.17.18.20 + 10.13.17.18.20 + 11.12.17.18.20 + 10.12.17.18.20 + 11.14.16.18.20 + 10.14.16.18.20 + 11.13.16.18.20 + 10.13.16.18.20 + 11.12.16.18.20 + 10.12.16.18.20 + 11.14.15.18.20 + 10.14.15.18.20 + (57) 11.13.15.18.20 + 10.13.15.18.20 + 11.12.15.18.20 + 10.12.15.18.20

The software also performed the automatic orthogonalization of the Lmodel. Now the logical product of any two logical summands in the new L-model equals zero, i.e. they are independent. The computer memory is limited, therefore the following limitations have been introduced: no more than 600 logical summands in the L-risk model, no more than 40 conjunctions in one, no more than 40 signs after the point in the value of the probabilities of events. The probabilistic risk model of the economic safety state of a country. The software ACM automatically replaced L-variables with their probabilities in the orthogonalized logical model. The negations of logical variables appear during orthogonalization; the probabilities of logical variables with negation equal Q=1–P.

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The machine notation of the P-risk model looks as follows: P{Y32}= P9.P11.P14.P17.P21 + P9.P10.Q11.P14.P17.P21 + P9.P11.P13.Q14.P17.P21 + P9.P10.Q11.P13.Q14.P17.P21 + P9.P11.P12.Q13.Q14.P17.P21 + P9.P10.Q11.P12.Q13.Q14.P17.P21 + P9.P11.P14.P16.Q17.P21 + 9.P10.Q11.P14.P16.Q17.P21_ + P9.P11.P13.Q14.P16.Q17.P21 + P9.P10.Q11.P13.Q14.P16.Q17.P21 + P9.P11.P12.Q13.Q14.P16.Q17.P21 + P9.P10.Q11.P12.Q13.Q14.P16.Q17.P21 + P9.P11.P14.P15.Q16.Q17.P21 + P9.P10.Q11.P14.P15.Q16.Q17.P21 + P9.P11.P13.Q14.P15.Q16.Q17.P21 + P9.P10.Q11.P13.Q14.P15.Q16.Q17.P21 + P9.P11.P12.Q13.Q14.P15.Q16.Q17.P21 + P9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P21 + Q9.P11.P14.P17.P19.P21 + Q9.P10.Q11.P14.P17.P19.P21 + Q9.P11.P13.Q14.P17.P19.P21 + Q9.P10.Q11.P13.Q14.P17.P19.P21 + Q9.P11.P12.Q13.Q14.P17.P19.P21 + Q9.P10.Q11.P12.Q13.Q14.P17.P19.P21 + Q9.P11.P14.P16.Q17.P19.P21 + Q9.P10.Q11.P14.P16.Q17.P19.P21 + Q9.P11.P13.Q14.P16.Q17.P19.P21 + Q9.P10.Q11.P13.Q14.P16.Q17.P19.P21 + Q9.P11.P12.Q13.Q14.P16.Q17.P19.P21 + Q9.P10.Q11.P12.Q13.Q14.P16.Q17.P19.P21 + Q9.P11.P14.P15.Q16.Q17.P19.P21 + Q9.P10.Q11.P14.P15.Q16.Q17.P19.P21 + Q9.P11.P13.Q14.P15.Q16.Q17.P19.P21 + Q9.P10.Q11.P13.Q14.P15.Q16.Q17.P19.P21 + Q9.P11.P12.Q13.Q14.P15.Q16.Q17.P19.P21 + Q9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P19.P21 + Q9.P11.P14.P17.P18.Q19.P21 + Q9.P10.Q11.P14.P17.P18.Q19.P21 + Q9.P11.P13.Q14.P17.P18.Q19.P21 + Q9.P10.Q11.P13.Q14.P17.P18.Q19.P21 + Q9.P11.P12.Q13.Q14.P17.P18.Q19.P21 + Q9.P10.Q11.P12.Q13.Q14.P17.P18.Q19.P21 + Q9.P11.P14.P16.Q17.P18.Q19.P21 + Q9.P10.Q11.P14.P16.Q17.P18.Q19.P21 + Q9.P11.P13.Q14.P16.Q17.P18.Q19.P21 + Q9.P10.Q11.P13.Q14.P16.Q17.P18.Q19.P21 + Q9.P11.P12.Q13.Q14.P16.Q17.P18.Q19.P21 + Q9.P10.Q11.P12.Q13.Q14.P16.Q17.P18.Q19.P21 + Q9.P11.P14.P15.Q16.Q17.P18.Q19.P21 + Q9.P10.Q11.P14.P15.Q16.Q17.P18.Q19.P21 + Q9.P11.P13.Q14.P15.Q16.Q17.P18.Q19.P21 + Q9.P10.Q11.P13.Q14.P15.Q16.Q17.P18.Q19.P21 + Q9.P11.P12.Q13.Q14.P15.Q16.Q17.P18.Q19.P21 + Q9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P18.Q19.P21 + P9.P11.P14.P17.P20.Q21 + P9.P10.Q11.P14.P17.P20.Q21 + P9.P11.P13.Q14.P17.P20.Q21 + 9.P10.Q11.P13.Q14.P17.P20.Q21 + P9.P11.P12.Q13.Q14.P17.P20.Q21 + P9.P10.Q11.P12.Q13.Q14.P17.P20.Q21 + P9.P11.P14.P16.Q17.P20.Q21 + P9.P10.Q11.P14.P16.Q17.P20.Q21 + P9.P11.P13.Q14.P16.Q17.P20.Q21 + P9.P10.Q11.P13.Q14.P16.Q17.P20.Q21 + P9.P11.P12.Q13.Q14.P16.Q17.P20.Q21 +

Logical and Probabilistic Management of Socioeconomic Safety

65

P9.P10.Q11.P12.Q13.Q14.P16.Q17.P20.Q21 + P9.P11.P14.P15.Q16.Q17.P20.Q21 + P9.P10.Q11.P14.P15.Q16.Q17.P20.Q21 + P9.P11.P13.Q14.P15.Q16.Q17.P20.Q21 + P9.P10.Q11.P13.Q14.P15.Q16.Q17.P20.Q21 + P9.P11.P12.Q13.Q14.P15.Q16.Q17.P20.Q21 + P9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P20.Q21 + Q9.P11.P14.P17.P19.P20.Q21 + Q9.P10.Q11.P14.P17.P19.P20.Q21 + Q9.P11.P13.Q14.P17.P19.P20.Q21 + Q9.P10.Q11.P13.Q14.P17.P19.P20.Q21 + Q9.P11.P12.Q13.Q14.P17.P19.P20.Q21 + Q9.P10.Q11.P12.Q13.Q14.P17.P19.P20.Q21 + Q9.P11.P14.P16.Q17.P19.P20.Q21 + Q9.P10.Q11.P14.P16.Q17.P19.P20.Q21 + Q9.P11.P13.Q14.P16.Q17.P19.P20.Q21 + Q9.P10.Q11.P13.Q14.P16.Q17.P19.P20.Q21 + Q9.P11.P12.Q13.Q14.P16.Q17.P19.P20.Q21 + Q9.P10.Q11.P12.Q13.Q14.P16.Q17.P19.P20.Q21 + Q9.P11.P14.P15.Q16.Q17.P19.P20.Q21 + Q9.P10.Q11.P14.P15.Q16.Q17.P19.P20.Q21 + Q9.P11.P13.Q14.P15.Q16.Q17.P19.P20.Q21 + Q9.P10.Q11.P13.Q14.P15.Q16.Q17.P19.P20.Q21 + Q9.P11.P12.Q13.Q14.P15.Q16.Q17.P19.P20.Q21 + Q9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P19.P20.Q21 + Q9.P11.P14.P17.P18.Q19.P20.Q21 + Q9.P10.Q11.P14.P17.P18.Q19.P20.Q21 + Q9.P11.P13.Q14.P17.P18.Q19.P20.Q21 + Q9.P10.Q11.P13.Q14.P17.P18.Q19.P20.Q21 + Q9.P11.P12.Q13.Q14.P17.P18.Q19.P20.Q21 + Q9.P10.Q11.P12.Q13.Q14.P17.P18.Q19.P20.Q21 + Q9.P11.P14.P16.Q17.P18.Q19.P20.Q21 + Q9.P10.Q11.P14.P16.Q17.P18.Q19.P20.Q21 + Q9.P11.P13.Q14.P16.Q17.P18.Q19.P20.Q21 + Q9.P10.Q11.P13.Q14.P16.Q17.P18.Q19.P20.Q21 + Q9.P11.P12.Q13.Q14.P16.Q17.P18.Q19.P20.Q21 + Q9.P10.Q11.P12.Q13.Q14.P16.Q17.P18.Q19.P20.Q21 + Q9.P11.P14.P15.Q16.Q17.P18.Q19.P20.Q21 + Q9.P10.Q11.P14.P15.Q16.Q17.P18.Q19.P20.Q21 + Q9.P11.P13.Q14.P15.Q16.Q17.P18.Q19.P20.Q21 + Q9.P10.Q11.P13.Q14.P15.Q16.Q17.P18.Q19.P20.Q21 + Q9.P11.P12.Q13.Q14.P15.Q16.Q17.P18.Q19.P20.Q21 + (58) Q9.P10.Q11.P12.Q13.Q14.P15.Q16.Q17.P18.Q19.P20.Q21

The probabilities of IE Y1 – Y21 were assessed by expert NIIinformation by the aggregate randomized indexes method. The assessments were made by all three experts, after which they were combined, taking into account the weights of the experts themselves (Table 6, second column). The following results were obtained by calculations:

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P31=0.3139 – the probability of housing construction success in Russia; P32=0.0252 – the probability of birth rate success in Russia; P33=0.0079 – the probability of economic safety of Russia.

2.1.2. LP-risk Analysis of Economic State For the purposes of the analysis of the current situation in Russia we have also calculated the significance of IE and their contributions to derivative events. For event Y33 we provide the machine script of these characteristics (Table 6). Table 6. Structural value of initiating events --------------------------------------------------------------------------Event Event Event The contribution The contribution number probability: value : to the minus to the plus : -----------------------------------------------------------------1 : 0.400000 : +7.22665E-03 : -2.89066E-03 : +4.33599E-03 : 2 : 0.400000 : +7.68871E-03 : -3.07549E-03 : +4.61323E-03 : 3 : 0.600000 : +2.81935E-03 : -1.69161E-03 : +1.12774E-03 : 4 : 0.150000 : +1.32675E-03 : -1.99013E-04 : +1.12774E-03 : 5 : 0.250000 : +1.50365E-03 : -3.75914E-04 : +1.12774E-03 : 6 : 0.450000 : +4.22834E-03 : -1.90275E-03 : +2.32559E-03 : 7 : 0.200000 : +2.58662E-02 : -5.17325E-03 : +2.06930E-02 : 8 : 0.300000 : +3.26686E-03 : -9.80057E-04 : +2.28680E-03 : 9 : 0.250000 : +2.63460E-02 : -6.58651E-03 : +1.97595E-02 : 10 : 0.400000 : +1.54433E-02 : -6.17733E-03 : +9.26599E-03 : 11 : 0.100000 : +1.02955E-02 : -1.02955E-03 : +9.26599E-03 : 12 : 0.300000 : +9.81296E-03 : -2.94389E-03 : +6.86907E-03 : 13 : 0.050000 : +7.24312E-03 : -3.62156E-04 : +6.88096E-03 : 14 : 0.300000 : +9.82995E-03 : -2.94898E-03 : +6.88096E-03 : 15 : 0.400000 : +4.86201E-03 : -1.94480E-03 : +2.91720E-03 : 16 : 0.250000 : +3.88961E-03 : -9.72402E-04 : +2.91720E-03 : 17 : 0.400000 : +4.87699E-03 : -1.95079E-03 : +2.92619E-03 : 18 : 0.300000 : +2.76228E-03 : -8.28683E-04 : +1.93359E-03 : 19 : 0.050000 : +2.15519E-03 : -1.07759E-04 : +2.04743E-03 : 20 : 0.100000 : +2.17600E-02 : -2.17600E-03 : +1.95840E-02 : 21 : 0.200000 : +2.58662E-02 : -5.17325E-03 : +2.06930E-02 : The significance and the contributions of repeated IE Y9 – economic stability in the country, which is part of models Y31 and Y32, are much

Logical and Probabilistic Management of Socioeconomic Safety

67

bigger than the significance of initiating events Y5 and Y16 with the same probability: x event Y9: significance = 0. 02634, contribution to minus = 0.0065, contribution to plus = + 0.01976; x event Y5: significance=0.0015, contribution to minus = - 0.00037, contribution to plus = + 0.00127.

2.1.3. LP-risk Management of Economic State LP-risk management of the economic health of a country is performed according to the results of qualitative LP-analysis of IE significance and contributions. After that, a decision is made about changing the probabilities of the most significant IEs. Resources are allocated for changing their probabilities, including staff skills development (Fig.9). Quantitative risk analysis on contributions parameter grades

Taking decisions about changing of most important parameters

Distribution of resources

Fig. 9. Scheme of risk management of the country’s economic safety

2.1.4. LP-management of Economic War with Sanctions Economic wars with sanctions belong to the problems of analysis and management, which are solved with the help of LP-risk models of SES economic safety. Natural competition determines the health of the economies of different countries in the global economic system. However, artificial influence on the economic health of a country can be exercised by means of economic sanctions. Examples of sanctions are the economic sanctions of the USA and EU against Russia and the counter-sanctions of Russia. The essence of the economic war with sanctions is that we would like to have minimal risk for our SES, while the opponent wants to increase it. In order to make a qualitative forecast of the economic health risk, borne due to the threats and sanctions of other countries, we have to build the LP-risk model of the economic health of a country and its SES. Then, using the LP-risk model of the SES state, we must calculate the contributions of IE to the “minus” and to the “plus” (39 – 42). By doing this we will be able to determine the most dangerous IEs and the ways to protect against them.

68

Chapter Two

For quantitative forecasting of the increase of economic health risk borne by a country due to the threats and sanctions against this country we have to build the LP-risk model of the economic health of the opponent country and its SES. Then, using the LP-risk model of the SES state we must calculate IEs’ contributions to the “minus” and to the “plus” (39 – 42). In this way we will find the most dangerous IE and choose the most effective sanctions. The search algorithm of the most dangerous initiating events and their combinations for SES state with L-connections of events and cycles might also look as follows. We must exclude one after another IE from the set of IEs, then a series of two IEs (all combinations of two IEs), etc. and calculate system risk change. In this manner we can determine the most dangerous IEs in the system and their combinations in twos, in threes, etc. Thus, LP-analysis of economic health risk and LP-management of economic health should be performed for a country and for its opponent countries. Having made the assessments and analysis of IE contributions to the economic health risk of a country, it should be decided which sanctions are the most dangerous ones and which sanctions should be introduced for the opponent country in order to cause its economic failure. Thus, top-economics considers not only the management of socioeconomic safety, but also some aspects of management of the national safety of the country, namely: 1. Methods of economic war with sanctions using LP-models of risk to socioeconomic systems (SES). 2. Hybrid LP-models of failure of the following significant SES to national safety: x Anti-corruption; x Combating drug addiction; x Management of the country’s innovation system. 3. Construction of the hybrid technology of LP-models for risk assessment and analysis of the failure of complex systems, processes and national security projects of the country.

2.1.5. LP-risk Management of Socioeconomic Evolution of Country LP-risk management of the economic development of a country is performed according to the scheme of complex systems management [12, 13]. The management presupposes control of the system’s movement along the pre-arranged trajectory and the making of corrections in case of deviations from it (Fig. 10). Here: j=1, 2, …, N – stages of development;

Logical and Probabilistic Management of Socioeconomic Safety

69

Pyi – economic state risk of a country, Uj – control actions (resources), Wj – corrective actions (resources). A socioeconomic system is transferred from the initial state A into the final state B along the chosen trajectory A – B during several stages. The development management program predicts potential troubles and provides resources for correction. The program calculates the values of parameters Pj, Uj, Wj at the stages of development N. The L-risk model of system development failure in total at all the stages:

Y = Y1 › Y2 › ... › Yn ,

(59)

where NOT Y1, NOT Y2 ,…, NOT Yn are the logical functions of system development failure (risk) at the stages. The P-risk model of the whole system development failure is written down on the basis of the L-risk model:

R ^Y = 0` = R1 + R2 ( 1  R1 )+ R3 ( 1  R1 ) ( 1  R2 )+ .... ,

(60)

where R1, R2, …, Rn are risks (probabilities) of events failure.

Fig. 10. Scheme of the system development management

2.1.6. Improvement and Correction of LP-risk Model The LP-risk model of the state of Russia, which was obtained by the combination of scenarios “Birth rate growth” and “Realty demand increase”, could be extended by adding such scenarios and corresponding LP-models as “Counteraction to bribery and corruption” and “Counteraction to drug addiction”, aimed at reducing economic losses in

70

Chapter Two

the country. We might also add the LP-models for managing the state of such SES as loan and operational risks of banks, the operation of companies, and the growth of profits in the country. For each of the mentioned scenarios we might build and study a hybrid LP-risk model of the failure to solve this difficult problem. Such a model includes random events (and logical variables), and the “wishes” and “possibilities” of the State, business, banks, scientists and public opinion. The subjects above have different wishes and different possibilities to solve the problem. Several hybrid models are discussed in [7, 8]. Calculation research showed that without scientists (developers of technologies, techniques and models) and public opinion (opposition and democratic forces with their access to mass media and TV) the difficult problems faced by Russia cannot be solved. The correction of the LP-risk model of the economic health of a country is made by changing the probabilities of IE Y1,…,Y21 both by statistical data and by expert NII-information as new signal events appear: x the change of system parameters and structure; x the change of investments in its development; x the emergence of new statistical data about the SES state; x the emergence of new events in economy, politics, law and innovations; x the skills development of the staff; x natural disasters or wars; x changes in the world market; x reforms in education, science and economy.

2.2. LP-management of the Country’s Innovations System We overindulge in difficulties and we have lost all our abilities to see obvious things. Thomas J. Peters

The management of the SES under study, belonging to the group SES1, which is of top priority for the country, is aimed at increasing revenues from industry and business. Russia occupies the 62nd position out of 142 in the world rating of innovations systems. We really must make an effort to improve the situation. Resources are needed for the management of the State and development of a country’s SES. Therefore, the innovations management system has to be developed in which technological innovations and management (including state management) amount to the same thing.

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71

The following sections are discussed below [17]: 1. The Global Innovative Index of the Russian Federation for 2013. 2. The development of the LP-model of the Global Innovative Index. 3. Analysis of the development of the innovation RMT SCS. 4. The development of the hybrid LP-risk model of the failure to solve the innovations problem. 5. The development of the indicative LP-risk model of the country’s innovations system state danger. An innovations system is characterized by a set of indicators. The indicators are normalized and their values are in the range [0, 1]. The value of the indicator qi (0 < qi) is considered as a deviation from the target or regulation. The value of indicator qi is considered as the probability of an event-proposition. We use the terms validity or invalidity of an index. In some cases, the index value deviation from 0 can be considered as a positive phenomenon and the validity event with the probability pi = qi. For the system we perform the logical addition of indexes of validity and determine the validity of the entire system. In other cases, the index value deviation from 0 can be considered as a negative phenomenon and the invalidity event with the probability pi = qi. For the system we also perform logical addition of indexes of invalidity and determine the invalidity of the entire system. Note: to retain the monotony of the LP-model of the system’s quality all indexes must be either valid or invalid. In studies of socioeconomic systems, we choose the term validity and invalidity by the prevailing practice in the subject area – to explore the success or non-success of systems. We assess the quality of the country’s innovation system by the GII method and the logical-probabilistic method, considering the validity of systems.

2.2.1. Global Innovative Index The Global Innovative Index (GII) is calculated on the basis of the Innovative Index of Possibilities (IIP) and the Innovative Index of Results (IIR) [24], each of which is based on the values of groups of validity factors (Table 7): x 7 groups of first level derivative factors Y1, Y2,,,,,Y7; x 21 groups of second level derivative factors Y11, Y12, Y13,…,Y71, Y72, Y73; x 84 initial factors of the lowest level Y111, Y112,Y113,...,Y731, Y732, Y733.

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Five groups of factors assess the possibilities of the innovations system: 1. Institutions – the State (political environment, regulative environment, business environment). 2. Human capital and research (education, science and development). 3. Infrastructure (information computer technologies, etc.). 4. Market (loans, investments, trade and competition). 5. Business (employees’ skills, the connection of business with innovations and knowledge). Two groups of factors assess the results of the innovations system: 6. Results of scientific research. 7. Results of the creative process. Each of 7 first level groups has several factors. The value of the group factor is calculated as the arithmetic mean of separate second level factors, included in it (there are 21 of them). Each second level factor is a function of initial factors (there are 84 of them in total). The following calculations have been carried out: 1. The innovative index of possibilities is calculated as the arithmetic mean of the first five groups of factors; 2. The innovative index of results is calculated as the arithmetic mean of the last two groups of factors; 3. The total GII is calculated as the arithmetic mean of the innovative index of possibilities and the innovative index of results; 4. The innovative efficiency coefficient is calculated as the ratio of the Innovative Index of Results and the Innovative Index of Possibilities. Table 7. The Global Innovative Index of the RF for 2013 Indexes Global Innovation Index Innovation Index of Possibilities Innovation Index of Results Innovations efficiency coefficient IIR/IIP Global innovation index for 2012 1 State 1.1 Political situation 1.2 Legal environment 1.3 Business environment

Identifiers GII-13 IIP IIR KEI GII-12 Y1 Y11 Y12 Y13

Score 37.2 30.6 43.8 0.7 37.9 56.0 42.9 57.2 68.0

Rank 62 72 52 104 51 87 117 100 55

Logical and Probabilistic Management of Socioeconomic Safety

2 Human assets and research 2.1 Education 2.2 Higher education 2.3 Research and development (R & D) 3 Infrastructure 3.1Information and communication technologies (ICT) 3.2 Common infrastructure 3.3 Environmental sustainability 4 Market 4.1 Credits 4.2 Investments 4.3 Trade and competition 5 Business 5.1 White collar workers 5.2 Innovative connections 5.3 Knowledge intake 6 Knowledge and technologies output 6.1Knowledge creation 6.2 Impact of knowledge 6.3 Knowledge diffusion 7 Creative outputs 7.1 Non-material assets 7.2 Creative goods and services 7.3 Online creative work

73

Y2.. Y21 Y22 Y23 Y3 Y31

44.1 62.0 40.0 30.3 37.2 59.6

33 42 46 31 49 28

Y32 Y33 Y4 Y41 Y42 Y43 Y5 Y51 Y52 Y53 Y6. Y61 Y62 Y63 Y7 Y71 Y72 Y73

32.0 20.1 45.4 23.6 37.1 75.6 36.1 58.2 18.9 31.2 30.4 34.6 33.0 25.7 30.8 27.0 32.2 37.1

57 115 74 116 32 78 52 34 109 52 48 25 77 68 101 125 81 44

Reports GII-2013 [24] and [31] provide the assessments of the innovations systems of 142 countries by 84 initial factors as the Score and the Rank. The higher the score of the innovations system of a country (in the interval from 0 to 100), the better is its innovations system. The ratings change conversely: the higher the score - the lower the rating. Table 8. The comparison of Global innovative indexes of countries Indexes GII IIP IIR KEI

Switzerland Score Rank

USA Score

Rank

Finland Score

Rank

China Score

Rank

Russia Score Rank

66.6 66.7 66.5 1.0

60.3 51.4 69.2 0.7

5 12 3 86

59.5 52.4 66.7 0.8

6 8 6 67

44.7 44.1 45.2 1.0

35 25 46 14

37.2 30.6 43.8 0.7

1 1 7 12

62 72 52 104

Chapter Two

74 Y1 Y11 Y12 Y13 Y2 Y21 Y22 Y23

87.3 92.7 97.8 90.2 94.6 92.3 94.7 10.1

16 6 6 6 12 12 11 39

86.0 79.3 79.3 77.0 94.6 88.3 90.2 8.0

17 25 44 21 13 16 17 1

95.3 97.9 100.0 100.0 96.8 95.9 100.0 10.1

2 1 1 1 6 9 1 39

48.3 39.2 49.0 41.7 50.3 44.3 34.8 27.4

113 126 106 58 116 89 87 118

56.0 42.9 57.2 68.0 44.1 62.0 40.0 30.3

87 117 100 55 33 42 46 31

The assessments of the derivative factors of the innovations system of Russia, GII, IIP and IIR, which can be found in Tables 7 and 8, demonstrate that Russia does not belong to 30 leading countries in terms of any IIP groups (the State, human capital and research, infrastructure, market, business, knowledge and technologies output, creative outputs). The following groups have the lowest rating: the State –87, market – 74, creative outputs – 101. The following factors of the IIP group have a low rating: regulatory environment – rating 100, loans – 116, trade and competition – 78, innovative connections – 109, knowledge impact – 77, higher education – 46, non-material assets – 125. The leaders according to GII (Switzerland, the USA, Finland), having the highest Rank (Table 8), are not keen to achieve the highest Score, as it is quite expensive.

2.2.2. Logic Global Innovative Index Score is used for the analysis of the innovations system of a country, and Rank is used for advertising purposes. There are a lot of initial factors — 84 — and it is difficult to decide how to manage the innovations system of a country. It is clear from the values of Score that there are no countries with all values of Score =100.0. The global innovative index GII, indexes IIP, IIR, derivative factors of the first and the second level and of the 84 initial factors, determine the condition and the attractiveness of the innovations system of a country, but they are not enough for managing the innovations system. GII and other derivative indexes are calculated by arithmetic addition with the averaging of initial factors. Arithmetic addition and the averaging of i-Score factors prevent us from finding the influence of each initial factor on GII and derivative factors. Logical events and logical efficiency functions in LGII. The Global Innovative Index (GII) is described by m=84 independent initial factors and their connections with derivative factors. The Michigan University

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75

report [24] provides the values of these initial factors for 142 countries. The ratings are determined on the basis of the values of the factors. Most initial factors have values in the interval [0, 100], which can be easily transformed into the interval [0, 1]. The values of other factors are also transformed into the interval [0, 1], i.e. all initial factors of validity can be normalized. Let us introduce the notion of an “valid event” as the deviation of the value of factor qi from the zero or set value. Let us assume that a validity event is the condition that the value of the factor is more than 0. qi t 0 (61) The value of the probability of this event equals the factor value. Initial factors and the corresponding events are independent and have the same weights for the GII system. wi 1/ m 1/ 84. (62) Normalized initial factors, which we will now call IEs, equal

qi

Scorei /100.

(63)

The criterion

Pi

qi ˜ wi

( Scorei /100) (1/ 84)

(64)

expresses the efficiency degree of the i-factor in the GII system and is the probability of the efficiency of the IE factor. Let us introduce the identifiers for L-variables of IE-factors (Table 8 and Table 9). In accordance with the data structure (Table 9 and Fig. 11) let us write down the L-functions of efficiency for derivative eventsfactors. Table 9. A fragment from the structure of the Global Valid Innovative Index of Russia Indexes Global Innovation Index Innovation Index of Possibilities Innovation Index of Results The innovations efficiency coefficient of IIR/IIP Global innovation index for 2012

Identif. GII-13 IIP IIR KEI

Score 37.2 30.6 43.8 0.7

Rank 62 72 52 104

GII-12

37.9

51

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Chapter Two

1 Institutions (the State) 1.1 Political situation 1.1.1 Political stability 1.1.2 Efficiency of the government 1.1.3 Freedom of press 1.2 Legal environment 1.2.1 Quality of legal regulations 1.2.2 Obligation of law 1.2.3 Dismissal of reservation cost 1.3 Business environment 1.3.1 Simplicity of starting a business 1.3.2 Simplicity of bankruptcy decision 1.3.3 Simplicity of tax payments

Y1 Y11 Y111 Y112 Y113 Y12 Y121 Y122 Y123 Y13 Y131 Y132 Y133

56.0 42.9 44.7 27.33 56.6 57.2 40.3 26.2 17.3 68.0 83.6 46.5 73.9

87 117 113 90 119 100 102 113 82 55 69 49 65

Let us begin the calculations of logical values LScore for derivative events-factors. This corresponds to mathematical and common sense. Using the logical addition of IE-factors, we will obtain the correct assessments of Score and Rank of all derivative events-factors in accordance with the structural scheme of the connection of events-factors (Fig. 11). The system of L-efficiency functions for 21 derivative events-factors of the second level:

­Y11 Y111 › Y112 › Y113 , ½ °Y ° ° 12 Y121 › Y122 › Y123 , ° °Y13 Y131 › Y132 › Y133 , ° ° ° °.............................. ° ® ¾ °............................. ° °Y71 Y711 › Y712 › Y713 , ° ° ° °Y72 Y721 › Y722 › Y723 , ° °Y ° ¯ 73 Y731 › Y732 › Y733 . ¿

(65)

The system of L-efficiency functions for 7 derivative events-factors of the first level:

Logical and Probabilistic Management of Socioeconomic Safety

­Y1 Y11 › Y12 › Y13 , ½ °........................... ° ° ° ® ¾ °........................... ° °¯Y7 Y71 › Y72 › Y73 .°¿

77

(66)

L-efficiency functions of the Innovative Index of Possibilities (IIP) and the Innovative Index of Results: LIIP Y1 › Y2 › ... › Y5 ; (67)

LIIR

Y6 › Y7 .

(68)

Conformity between the global logical and scoring innovative indexes looks as follows: LGII ˜100 o SGII . (69) Note. Let there be an L-function of validity for events:

Y

Z1 › Z 2 › Z 3 › Z 4 . The L-function of validity in the equivalent orthogonal form:

Y

Z1 › Z 2 Z1 › Z 3 Z 2 Z1 › Z 4 Z 3 Z 2 Z1.

The probabilistic function of validity for the system: P(Y)=P1 + P2(1 –P1) + P3(1 –P1)(1 –P2) + P4(1 –P1)(1 –P2)(1 –P3), where P1, P2, P3, P4 – the probabilities of events Z1, Z2, Z3, Z4.

Chapter Two

Fig.11. The structural scheme of events-factors connection for LGII

78

Logical and Probabilistic Management of Socioeconomic Safety

79

LP-analysis and management of LGII and derivative events-factors is performed using P-models. Quantitative analysis consists in determining the significance of initiating events-factors in the probabilities of derivative events-factors. The significance of IE and their combinations is defined by the change of probabilities of LGII and derivative events during their exclusion [12, 13]. For the innovations system the management of LGII state is considered. The management is performed according to the results of the analysis of IE significance in the following order: the assessment of events-factors’ significance, the selection of the most important ones, the allocation of resources for the change of probabilities of these eventsfactors. The management of LGII development is conducted through the management of the movement along the selected trajectory and corrections in case of deviations from it. We have made the calculations of logical innovative indexes in the developed program in Excel. If we compare the calculations results by GII and LGII techniques (Table 10), it is obvious that global innovative indexes differ in different techniques. Table 10. Comparison of calculations results by GII and LGII techniques (data from 2013) Indexes

Identifiers

Score (points)

37.2

Probability of efficiency, P 0.334138

Global Innovation Index Innovation Index of Possibilities Innovation Index of Results 1 State 1.1 Political situation 1.2 Managed environment 1.3 Business environment 2 Human assets and research 3 Infrastructure

GII-13

*AScore,(9)

33.4

IIP

30.6

0.248174

24.8

IIR

43.8

0.114341

11.43

Y1 Y11 Y12

56.0 42.9 57.2

0.04847 0.015176 0.009988

4.847 1.5176 0.9988

Y13

68.0

0.02406

2.406

Y2

44.1

0.051567

5.1567

Y3

37.2

0.057438

5.7438

Chapter Two

80

4 Market 5 Business 6 Output of knowledge and technologies 7 Creative outputs

Y4 Y5 Y6

45.4 36.1 30.4

0.050785 0.06886 0.060265

5.078 6.886 6.0265

Y7

30.8

0.057543

5.05754

Logical innovative indexes of derivative events groups of the first level are nearly 7 times less than LGII, and logical innovative indexes of derivative events of the second level are about 4 times less than those of the first level. The Logical Innovative Index of Possibilities is about 2.5 times higher than the logical Innovative Index of Results (in GII the relation of those indexes equals 0.7). The comparison of results shows that they correspond to common sense and LP-calculus rules [9]. The advantages of the LP-model of LGII. The LP-model of LGII provides an effective technique of assessment, analysis and management of the innovations system of a country. In the corresponding GII technique (Tables 8—9) all derivative factors at all levels have practically the same Score values (in points), which are equal to the average Score value of initial factors (~50.0). The influence of initial factors is averaged. It is impossible to analyze and manage separate initial factors correctly. The proposed LP-model of LGII has the following advantages: 1. It provides the accumulation of the values of assessments of LScore for derivative events-factors. At different levels they become different depending on the number of the factors of IE. 2. Derivative events-factors of the 2nd and other higher levels have an accurate assessment of their attractiveness and utility and could be used for analysis and management by the allocation of resources to change them. 3. The innovative indexes of possibilities and results have totally different LScores, which correspond to common sense and the number of IE affecting them. 4. The innovative indexes of the groups of events-factors have correct assessments because they are calculated without averaging and could be used effectively for managing the innovations system of a country. Arithmetic AGII and the proposed logical LGII do not include all the aspects of the effective management of the innovations system of a country. It is not clear what should be done in order to improve the quality of the innovations system and what role the State, business, banks,

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scientists and public opinion play in the solution of this problem. These questions could be answered only by analysis of examples of real innovations.

2.2.3. Analysis of the Development and Evaluation of Innovation of RMT SCS Let us discuss the drawbacks of the innovations system in the country, which were revealed in the process of the development of the innovation “Risk management technologies in structurally complex systems (RMT SCS)” [17]. Links with foreign scientists. RMT SCS was tested during eleven annual International Science Schools “Modeling and analysis of safety and risk in complex systems” (ɆȺSR), which were organized in 2001 by the Laboratory of Integrated CAD Systems of the Institute of the Problems of Mechanical Engineering, RAS. About 150 scholars (including 30 from abroad) took part in the Schools. More than 1100 talks were given. They were devoted to the problems of safety and risk in engineering and the economy. The author as one of the organizers took part in compiling the programmes of the schools and in publishing the proceedings. Scientists from Great Britain, the USA, Japan, India, the Ukraine, etc. took a special interest in LP-models for managing risk and efficiency in the economy and in banks. In spite of the success of the Schools and the participation of numerous Russian and foreign scientists [32], the Russian Foundation for Fundamental Research (RFFR), for economic reasons, in 2011 stopped giving grants for the organization of the Schools. Only incompetent State and RAS officials could do that. The links with Western scholars were broken; the communication devoted to a most important problem was stopped. The officials say that applications for organizing conferences should be filed three months before. It is obvious that it is impossible to organize a conference at such short notice, that foreign scholars usually plan their time and look for finances one year ahead. Fundamental and applied directions of science development in Russia. Top priority directions of scientific research in Russia are the ones which encourage the development and stability of the country. The fundamental scientific directions, as seen by the government, fail to encourage the sustainable development of the country. Top priority directions of scientific research in Russia do not include the safety of SES; counteraction to corruption; bribery and drug abuse; management of loan and operational risks by Basel; assessment of the

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operation of companies and enterprises in accordance with the WTO; the management of the condition and development of SES and the State. At the same time the following socioeconomic problems do exist in the country: x Economic stagnation. x Corruption and larceny are thriving in management and business. x Drug abuse is growing – Russia now leads the world in drug usage. x Russia lacks an effective innovations support system. x Russia lacks effective management of socioeconomic systems. x Scientists and public opinion play a very small part in solving problems, etc. Investments in other “top priority fundamental problems” will be pilfered, if the current situation with corruption does not improve. The concept of sustainable socioeconomic development of the country. When we choose the aim of successful development of SES and of a country we should use the social justice concept [13, 30]. The Nobel dynasty in Russia was among the first to introduce the social justice concept at their enterprises. Three generations of the Nobels worked in Russia in the 19th and early 20th centuries. In 1917 the Nobels had to return to Sweden. Wasn’t it the reason why Sweden became the model for the State based on social justice? The Nobels’ social justice policy meant that they spent a significant share of their profits (from diesel production, oil and gas extraction and transportation, etc.) on their employees’ needs. They paid them decent salaries, introduced the eight hour working day, built accommodation, schools and kindergartens, provided their workers with a free medical service, etc. They trained skilled workers and invested money in education, science and innovations in production. The successful development of Russia is also possible on the basis of the social justice concept. To get revenues the State mainly uses natural resources (oil, gas, timber, etc.). A lot of workers and clerks are employed in the extraction, transportation, refinery and sale of these resources in production enterprises, banks, insurance companies, etc. Social justice means decent salaries and pensions for these people, and caring about their daily problems, education, medical service, etc. It is generally understood that the successful development of SES and a country is closely connected with social justice. However, we know some examples of the successful development of economies based on the military establishment.

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Scientists and public opinion in the solution of socioeconomic problems. The well-known scientists James Buchanan and James Heckman were awarded Nobel prizes for creating models connecting economics and politics. We have substantially developed their ideas. We have introduced signal events in economics, politics, innovations and law, as well as events connected with the behavior and actions of the State, business, banks, scientists and public opinion into LP-models of the sustainable development of a country and SES. It might seem that our propositions should have attracted attention and led to effective decisions in the management of SES and the country. However, they were not needed and received no support, because they were considered second-rate and irrelevant. Scientists are very often asked to substantiate the service life extension of used and obsolete equipment in power economy, metallurgy, chemistry, etc. Thus, the blame for potential accidents is shifted onto them. Scientists created the LP-risk model of employees’ bribes and fraud, built the LP-risk model of bribes in an office allocating resources and granting permits, and the LP-model of revealing bribes by service parameters. They also proposed effective models for action to counter drug addiction among the population of the regions, for the management of SES state and its development. However, these projects were rejected by State and RAS officials. A paper on LP-models of corruption and bribes could not be published in Russia for three years since 2005. After its publication in this country it was published in a number of foreign academic journals. The leaders of the country began referring to the main ideas of the article and promised to solve the problem. Tough luck! This problem cannot be solved without laborious LP-programs. However, State and RAS officials did not care about the certification of techniques and programs. The complex event of the failure of subjects (the State, business, banks, scientists and public opinion) taking part in the solution of socioeconomic problems can be represented as the logical addition of events “lack of wishes” and “lack of possibilities”, having the probabilities of those events. Events failure risks are different for different subjects. Some subjects do not wish to solve the problem at all. The Nobel Prize winner J. Buchanan discussed the situations when it is beneficial for the State to cooperate with crime and corruption. In order to fight an incompetent government, cooperating with corruption, the wishes and possibilities of public opinion are needed. Public opinion has a wish to solve the socioeconomic problem in the interests of society. It realizes its possibilities via democratic institutions,

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opposition, mass media, meetings, demonstrations, etc. Computer simulation demonstrated that it is impossible to solve Russia’s difficult socioeconomic problems without scientists and public opinion. Russian science has been divided into clans by State and RAS officials. A lot of new science centres and institutes have appeared. It is common knowledge that science and innovations develop at the intersection of allied disciplines. The scientific direction RMT SCS appeared at the intersection of technical, economic, social and information problems. State and RAS officials refuse to give grants to the developers of this direction in science, claiming that they do not work in the required department of RAS, their research is not prestigious, the technologies are not fundamental research, etc. The Western world lives by developing and selling technologies. Russian State and RAS officials do not consider “technologies” to be fundamental developments. However, the discipline “Technology” was included in the curriculum of gymnasium students in Russia before 1917, ɚnd the Massachusetts Institute of Technology gave the world the greatest number of Nobel Prize winners. The RMT SCS innovation was not financed under its own name, though some money was allocated in RAS programmes of “fundamental” character. Financing of science. State and RAS officials are particularly “skillful” at allocating funds for fundamental and applied research of the problem. Every year scientists of academic institutes are to make plans including “fundamental” topics of research, otherwise they will be given no money. The titles of research topics are very long and vague; academicians are begging the government for money. The absurdity of this situation is obvious: fundamental problems do not appear every year and they cannot be solved during one year. Academicians and their institutes formulate topics of top priority research directions, as well as the demands for grants competitions. They do it only in their own interests. The fundamental research direction RMT SCS does not exist for them. Therefore a costly certification of methods and programs is required, but nobody is going to provide these funds. The Skolkovo Program is of no use for most innovative scientific projects, because one of its demands is to provide the documents confirming the participation of a business joint contractor in the financing of the project. Social and economic problems, determining the sustainability of the country’s development, are not on the list of Skolkovo top priority problems. The domination of Moscow also affects financial aspects. The officials never forget to finance their patronized academic clans and their inner circle. Constructive proposals to the upper echelons of power have

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been met with funny run-around replies like “We are dealing with it” (the bribery problem). The application of Western methods, programmes and techniques. Let us describe the examples of borrowing Western methods, programmes and techniques. On 25 October 1886 at the meeting of the Academic Board of Kazan University P.S. Poretsky gave a talk [11] devoted to the solution of the general problem of the probabilities theory with the help of mathematical logic. In 1917 N. Bernstein published a paper in which he extended the axiomatic of Boolean logic to the axiomatic of events. Kolmogorov (1929) introduced axiomatic for probabilities as one of possible measures. In 1939 V. I. Glivenko published a paper in which he made generalizations of the axiomatic. I. A. Ryabinin introduced the axiomatic of LP-calculus and the analysis of the reliability of engineering systems [9]. Some Russian scientists caught up with the new fashionable Western trend “Bayesian networks”, which has no effective applications. RAS and State officials have been supporting this trend with RAS grants for several years. The developers of RMT SCS, following in the footsteps of Russian scientists from P. S. Poretsky to I. A. Ryabinin, have been awarded no grants from RAS. The Bologna process. The officials from the Ministry of Education have been implementing the Bologna process in the curriculum of universities. These are the programmes of disciplines and lists of competencies (what the future specialist must know). We have made ourselves familiar with these materials and realize that they do not use the notions of risk, safety and sustainability; and they ignore such phenomena of Russian life as corruption, bribery, kickbacks, etc. Where are the graduates of our universities supposed to work then? Citation and the number of co-authors. The number of citations from the works of scientists in Russian and foreign journals was introduced by RAS and State officials as the criterion of the quality of universities’ work. It led to the fact that some papers by scientists from universities and RAS institutes, even those devoted to not very important subjects, have up to five authors. Collective work not only breeds the illusion of creative effort, but is also a sign of hackwork, giving a good cause for investigations into this problem. Non-transparency of methods and closed nature of software. RAS and State officials promoted the implementation of non-transparent Western methods of assessing credit risks and ratings and corresponding software [33]. The Central Bank of the Russian Federation forces all banks to use it under the threat of financial audit and punishment. The banks,

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buying expensive software, content themselves with information only from promotional leaflets. The methods are a commercial secret. The software is based on closed source, which makes it impossible to understand either the functions realization mechanism, or the interaction of software units, or the algorithms, because they are closed [33]. The wishes and possibilities of subjects in the solution of problems. State and RAS officials propose that scientists should implement innovations in business and production. Let us demonstrate, using the example of the innovation of counteraction to corruption, that it is impossible to do it with the existing structure of economy and science management. The LP-risk model of the failure to solve problems. They combine the scenarios of subjects’ failure (the State, business, banks, scientists and public opinion), taking part in the solution of the problem, and the scenarios of failure of objects-problems, constituting the core of the problem [8, 12, 21]. A complex event of the subjects’ failure is represented as the logical addition of events “lack of wishes” and “lack of possibilities”. The risks of events failure are different for different subjects. Some subjects do not wish to solve the problem at all. The Nobel Prize winner J. Buchanan showed that it is beneficial for the State to cooperate with corruption and crime when it does not have enough specialists and resources for management. Therefore the wishes and possibilities of public opinion are needed to fight with the incompetent government and its cooperation with corruption. The State. It includes the Presidential Administration, the Government, the State Duma, etc. They demonstrate their wish to solve a problem by numerous declarations and by creating various committees. The possibilities to solve the problem are limited, as they have no real wish and knowledge to do it. The officials at all levels are not interested in solving the bribery and corruption problem. They make new laws for solving it. Laws often breed a new generation of bribe takers and do not offer problem solving technologies. We should change our priorities and, besides special investigation activities, use simple technologies for revealing corruption by statistical data. Business. Two subjects are involved in a bribe: a giver and a taker. Both of them have their own benefits. The giver solves his predicament faster, better, gets privileges and evades the law. The taker gets the money, etc. Businessmen have a wish to make money – more, faster, by

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all methods and they also want to survive the competition. However, they are interested in constant rules of the game. The State as the regulator must keep business within appropriate boundaries. Economic crime agencies of the regions are not interested in effective counteraction to bribery and corruption. They are content with the special investigation activities system, which yields big profits. They usually know all bribe takers and bribe givers and the amount of money involved, but very few criminal cases are initiated, which proves the fact that they are bribe takers themselves. Scientists created the LP-risk model of employees’ fraud, and built the LP-risk model of bribes in an office granting resources and giving permits and the LP-model of revealing bribes by service parameters. However, State and RAS officials took no interest in their work. Public opinion has a wish to solve the problem of bribes and corruption. It realizes its possibilities to change the situation via democratic institutions, opposition, mass media (newspapers and TV), meetings, demonstrations, etc. However, democratic institutions and opposition in the country are not strong enough and cannot counteract the power of the State. Computer simulation demonstrated that it is impossible to solve difficult Russian socioeconomic problems, for example counteraction to drug addiction, without scientists and public opinion. The management of credit provision process. Economic development, creation and implementation of innovations are impossible without attracting available loans. However, the high interest rate is an obstacle. In Russia loan interest rates for business are 10.5—17 %, while in Europe they are 3–4 %. The developed LP-models for assessment, analysis and management of loan risk allow us to reach European rates, but the banks do not want to apply them. Firstly, they need the decision of the Central Bank; secondly, the banks do not bother themselves with exact risk assessment and analysis and prefer to shift loan risks onto their clients. They do it by demanding loan collateral and by increasing loan interest rates (possible losses are compensated by profits, which take into account possible losses due to risk and insurance expenditure). Counteraction to corruption and drug addiction. Russia is the leader in the average per capita consumption of heroin, which is more than three times higher than in Europe. According to UNO data, Iran intercepts 20 % of opiates entering the country, China – 18 %, Pakistan – 17 % and Russia – only 4 %. The drug abuse situation is critical. More than 100,000 people die of drug abuse, which is the highest number in the world [34, 35].

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The problem of assessing the danger of drug addiction is quite a complex one and it has been discussed in various publications. A special UN committee deals with the assessment and analysis of drug abuse in different countries. The known methods of drug abuse assessment and analysis, as the survey of the methodological support of monitoring systems showed, are not transparent and adequate to events and risk. Drug abuse and corruption are closely connected, as the drug business is highly profitable. We have developed a hybrid LP-risk model of the failure to solve the drug addiction problem (with and without corruption), a conceptual LPmodel forecasting the risk of drug addiction development, and an indicative LP-risk model of drug abuse danger, taking into account the latent character of drug abuse. We have made a risk assessment of the danger of drug abuse for a real region, on the basis of monitoring data. Losses caused by drug addiction and corruption are great; however, State and RAS officials do not consider the problems of corruption and drug abuse to be fundamental in character and they do not include them in the list of top priority scientific problems. It was impossible to get any grants for research into this problem. On the basis of the analysis we have conducted and the development of RMT SCS a conclusion could be made that, in addition to the already existing LP-model of the Global Innovative Index, we have to create LPmodels for the analysis and management of the innovations system, namely: 1. A hybrid LP-risk model of the failure to solve the innovations problem of the country. 2. An indicative LP-risk model of the danger of the innovations system’s condition.

2.2.4. Hybrid LP-model of Failure of Solution of Innovation Problem The hybrid LP-risk model combines risk scenarios for subjects and objects [12, 21]. The failure to solve this difficult problem DPinn depends on subjects S1, S2,…, S5, taking part in the solution to the problem, and objects – tasks Tinn(T1,T2,T3) — constituting the core of the problem. The subjects determine who is to solve the problem, and “the objects” – which tasks are solved in the problem DPinn (Fig. 12).

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Fig.12. The hybrid LP-risk model of failure

The objects-tasks constituting the core the problem include: T1 – determination of the factors of the system of innovations in the country; T2 – the creation of the conceptual LP-model forecasting the risk of the system of innovations development; T3 – the creation of the indicative LP-risk model of the danger of the condition of the particular innovation’s development and implementation. Failure events and logical variables, denoted by the same identifiers, are connected with objects and subjects. The failure to solve a difficult problem is formulated as follows: the failure of the event happens due to the failure of events DPinn, Sinn, Tinn, S1, S2,…,S5; T1, T2, T3, which are connected failure events and logical variables. We denote them by the same identifiers. The scenario of a failure to solve the difficult problem DPinn is formulated as follows: the failure of the event DPinn is due to the failure of the event Sinn OR Tinn. The logical functions of the system of innovations failure in the country are: DPinn Siin š Tinn ; Sinn S1 › S2 › ... › S5 ; Tinn T1 › T2 › T3 . (70)

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The probabilities of IE S1,S2,…,S5; T1, T2, T3 are assessed by the randomized aggregate factors method, using expert NII-information [14]. The scenarios for the subjects of the LP-risk model are created, taking into account their wishes and possibilities. Structural, logical and probabilistic risk models are developed for the risk models of objectstasks. Let us describe the scenarios of the behavior of the subjects taking part in the solution of the innovations problem. We will use those scenarios for building LP-risk models and for the assessment of events probabilities by NII-expert information. The State S1. It includes the President, the Government, the State Duma, and the Federation Council. The State demonstrates its wish W1 to solve the problem in numerous declarations of its leaders and by creating committees, laws and regulations. Possibilities O1 to solve the problem are limited due to the lack of resources and specialists; State bodies have no notion and knowledge of risk management technologies. Business S2. The wish W2 of business is to make as much money as possible, quickly, by any means and to survive the competition. Business will support only those innovations which will bring profit in the immediate future. The State as the regulator can induce business to allocate a certain share of the profits to the innovations fund. Banks S3. The wish W3 of banks is to make as much money as possible and to survive the competition. Banks are interested in granting credit for innovations, which will bring them profit without any risk. The State as the regulator can induce banks to allocate a certain share of the profits to the innovations fund. Scientists S4 for the purposes of analysis and management of the innovations support system have created a hybrid and an indicative LPmodel, as well as the corresponding software complexes. Public opinion S5. The risks of the failure of events, depending on the criteria “lack of wishes” and “lack of possibilities” are, naturally, different for different subjects. Some subjects do not wish to solve the problem at all. The Nobel Prize winner J. Buchanan studied such situations. Therefore, the wishes and possibilities of scientists and public opinion are needed in order to fight with the incompetent Government. Public opinion S5 has a wish W5 to solve the problem of innovations in the country. It can encourage the State, business, banks and scientists to develop and implement the system of innovations in the interests of the population of the country. It realizes its possibilities O5 via democratic institutions, opposition, mass media (TV, newspapers), meetings, demonstrations, etc.

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2.2.5. Indicative LP-model of State Danger of Innovation System Analysis of RMT SCS development and implementation allows us to define the characteristics of the system of innovations failure (see Table 11). Table 11. The characteristics of the system of innovations failure ʋ 1 2 3 4 5 6 7 8 9 10 11

Characteristic Communication with foreign scientists Identification of top-priority fundamental and applied research The concept of the development of socioeconomic systems and the country The involvement of scholars and public opinion in the solution of complex socioeconomic problems The creation of innovation projects at the confluence of sciences The adoption of foreign methods, programs and techniques The analysis of wishes and possibilities of the subjects participating in the solution of the problem Credit provision management Funding of science and innovation projects Formation of an orders bank for fundamental applied projects and research from companies and ministries The share of the country’s gross output allocated in the fund for innovations and science

Indentifier Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11

The list of characteristics might change in the process of the development and implementation of other innovations. The indicative LP-risk model of the system of innovations failure is based on the indicative factors which characterize the failure of the system of innovations (Table 11). Indicative factors-events are defined in general, without any details. The risks (probabilities) of these events, defining the innovations system failure, could be assessed by expert information, using the aggregate randomized factors method [14]. The indicative LP-risk model of the system of innovations failure is verbally defined as follows: failure risk happens either due to any eventfactor, or due to any two events-factors, or due to all events-factors.

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The indicative risk model of the system of innovations state danger: Z1 › Z 2 › Z 3 › Z 4 › Z 5 › Z 6 › Z 7 › Z8 › Z 9 › Z10 › Z11 . (71)

The indicative probabilistic risk model of the system of innovations state danger: P{Y } R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 )  ..., (72) where Rn is the risks of events-factors Zn, n=1,2,…,11. The methods of LP-analysis and LP-risk management in systems are described in detail in [12, 13]. We would only like to point out that the simple structure of expressions (71)–(72) allows us to think that the significance and the contributions of initiating events-factors Z in the system of innovations failure risk are proportional to the value of their risk. The management of risk consists in reducing the risk of the most significant initiating events-factors through structural changes in economy, science and education and allocating resources for reducing the risks of these events. Conclusion. The aim of the system of innovations is to reduce economic losses and to increase profits. For the purposes of the innovations system management the following investigations and research were carried out: 1. Analysis of the Global Innovative Index was conducted and its main methodological drawbacks were revealed. 2. The Logical and Probabilistic Global Innovative Index (LGII) was developed. It has a number of advantages for solving the problems of the analysis and management of the system of innovations. 3. The analysis of the system of innovations of a country was conducted through the example of the development and implementation of the innovation “Risk management technologies in structurally complex systems”. 4. The hybrid LP-risk model of the failure to solve the problem of innovations in the country with the participation of the state, business, economy, scientists and public opinion was developed. 5. The indicative LP-risk model of the system of innovations state danger was developed. 6. It was found out that it is impossible to solve the difficult socioeconomic problems of Russia without the participation of scientists and public opinion.

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7. It was demonstrated that, in order to develop and implement innovations on the basis of fundamental and applied research, reforms in education, science and economy are needed.

2.3. LP-models for Counteraction against Corruption Everyone is capable of fraud in a difficult life situation, if the valuables are not taken good care of and the theft can be concealed for some time. W. Albrecht, J. Wentz, T. Williams

The management of the SES under study, belonging to the group of top priority SES-1, is aimed at reducing economic losses from bribes, theft and corruption and improving the spiritual welfare of society. According to official estimates corruption increases the cost of goods and services by 5–15 %; damage caused by corruption amounts to 20 – 25 bln. dollars a year. We propose LP-risk models for the economic crime counteraction service of a city or a region with the aim of revealing, assessing and analyzing bribery by statistical data. The following LP-bribery models will be described: 1) in an office, based on the results of its operation; 2) of officials on the basis of their behavior description; 3) of the office and civil servants on the basis of service parameters analysis. We will provide examples of training and analysis of LP-bribery models according to statistical data. The problems regarding bribery and corruption have high computational complexity and are solved only with the help of the computer and special software. The problem of bribery and corruption is important in all countries.The word “bribe” appeared in Russia during the Tartar Yoke. At present the website www.vzyatka.ru informs its visitors about the well-doing of bribery and corruption. A lot of articles have unusual titles, such as “The Power of the Bribe”, “Bribes Capture Cities”, “The Bribe as the Force for Progress”, etc. The first textbook devoted to bribery and corruption appeared: “Anticorruption Policy” was written by a group of authors, led by the economist Georgy Satarov. The books and articles devoted to corruption and bribery contain deep detailed descriptions and analysis, many different examples, and

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commentaries on laws and the Criminal Code, but lack mathematical models of bribes. Mathematicians and engineers can solve the extremely complex tasks of building and controlling planes, ships, etc., but they have not done anything for solving such burning issues as revealing fraud, bribery and corruption. Adequate mathematical tools are needed for solving these problems. Differential and integral calculus is taught at universities, but students do not get enough knowledge of logic, discrete mathematics and combinatorics, which, according to John von Neumann and Norbert Wiener [25, 26], are more suitable for solving socioeconomic problems. Such adequate mathematical tools have been created in “Risk management technologies in structurally complex systems” [12, 13]. They have been tested for the assessment and analysis of credit risks, security portfolio risk, the risk of efficiency loss, and the risk of the failure of a company’s management. LP-risk models are highly efficient. For example, LP-models of credit risk proved to be twice as accurate and seven times as robust and transparent in recognizing good and bad loans as the already available methods. In the present work we use the LP-approach and LP-calculus for solving an important problem – counteraction to bribery and corruption.

2.3.1. Axioms for Counteraction against Bribery and Corruption Corruption is considered to be one of the main types of shadow economy. Corruption is usually understood as the receiving of bribes and illegal profits by State officials, who extract them from people for the sake of personal wealth accumulation. Bribery and corruption are a blatant disregard of civil ethics and legislation. The following provisions and axioms have been adopted for creating a system and technologies of counteraction to bribery and corruption [13, 37]: x Everyone is capable of a fraud in a difficult life situation, if the fraud can be temporarily concealed and if the reasonableness of decisions taken is not controlled adequately. x Counteraction to fraud, bribery and corruption is impossible without quantitative assessment and analysis of the probability of bribery. x Every commercial bank and company can take bribes if its business is not transparent and there is not enough control over it. x Fraud and bribery stand behind the methods of assessing credit risks and the ratings of banks and loan debtors.

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x The complex organizational structure of an office or a company is a sign of fraud and corruption. Let us explain the first axiom by an example [37]. The honorable USA President Abraham Lincoln once threw out of his study a person who had offered him a large bribe. When asked what had put him out of temper he replied: “Everybody has his own price and that man got too close to mine!” The notion of the probability of bribery and corruption is close to the notions of reliability and safety in technology, as well as to the notions of fraud and risk in economy, business and banks. Bribes are most often given when the following documents are required: licenses (education, tourism, medicine, construction), permits (traffic police, customs), educational certificates and diplomas, registrations (police, embassies, local authorities). Scenarios and technologies of bribes are different for a ministry, for the Mayor’s office, for a company, a bank, a civil servant, a doctor, a teacher, etc. A bribe involves two objects: a giver and a taker, and they both have their own benefits. A bribe giver solves his problem faster, better, receives privileges and evades the law. A bribe taker has financial benefits, gets a payoff, etc. The following terms are used below: bribe and corruption probability, success and failure probability, bribe probability, good or bad project probability (object, civil servant, office) from the point of view of bribery probability. For quantitative assessment and analysis of bribery probabilities the LP-risk theory, with incompatible events groups (IEG) and LP-bribery models, is built on the basis of statistical data [38]. It is the first mathematical work devoted to bribery and the corruption risk theory. It deals with the problems of modeling, assessment and analysis of bribery and corruption risk and nearly totally omits social, legal and organizational problems.

2.3.2. Hybrid LP-model of Failure in Counteracting Corruption Events and probabilities. A bribery event can be described by signs and their grades, which are random values and treated as logical variables and random events-signs and events-grades with their own probabilities. Events-signs are linked by logical connections OR, AND and can have cycles. Event-grades for a sign constitute an IEG [12, 13]. The logical variable Zj, corresponding to the event-sign, equals 0 with probability Pj, if sign j proves the presence of a bribe, and equals 1 with

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probability Qj=1–Pj when there is no bribe. The logical variable Zjr , corresponding to gradation r for sign j, equals 0 with probability Pjr and equals 1 with probability Qjr=1–Pjr. The vector Z(i)=(Z1,…, Zj,…, Zn) describes the object i from statistics. For the object i instead of L-variables Z1,…,Zj,…,Zn we have to put L-variables Zjr for the grades of signs of this very object. The L-function of bribery risk in general terms: DP S š T ; S S1 › S 2 › ... › S5 ; T T1 › T2 › T3 . (73) The P-function of bribery risk in general terms

P{DP

0}  P{T

0} P{S

P{S

0}

P{T

0} P{T 1

P{S 1

0}  P{S

2

0}  P{T 2

0}(1  P{S 1

0}(1  P{T 1

0}; 0})  P{S 3

0})  P{T 3

(74) 0}(1  P{S 1

0})(1  P{S

0}(1  P{T 1

Pi(Y=1|Z(i)) = P(P1, …, Pj, …, Pn), i=1,2,…,N.

2

0})  ...;

0})(1  P{T 2

0}).

(75)

For each event-gradation in IEG three probabilities are considered: P2jr – relative frequency in statistics; P1jr – the probability in IEG; Pjr – the probability which replaces probability Pj. The LP-bribery model training by statistical data. The task of identification (training) of the LP-bribery model by statistical data is one of the main and most difficult ones in the bribery problem. It can be solved by algorithmic methods [13]. The following scheme for solving the task has been proposed. Let the probabilities of grades Pjr, r=1,2, …, Nj; j=1,2,…,n be known in the first approximation and risks Pi, i=1,…,N be calculated for projects in statistics, each of which could be accompanied by a bribe. Let us define admissible risk Pad (Fig. 3), so that the accepted design number of projects without bribes (good projects) Ngc would have the value of risk lower than admissible and correspondingly the number of projects with bribes (bad projects) Nbc = N – Ngc would have the value of risk higher than admissible. At the optimization step let us change probabilities Pjr, r=1,2,…,Nj; j=1,2,…,n, so that the number of correctly recognized projects with and without bribes would grow. The analysis of bribery probabilities. Suppose the P-bribery model has been trained and probabilities Pjr are known. Let us define the contributions of events-signs and events-grades to bribery probability for a project and a set of projects, and to the accuracy of the LP-bribe model. For this purpose let us calculate the differences between the values of

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characteristics for the optimal model if the probabilities of corresponding events-grades are given zero values.

2.3.3. LP-model to Counter Bribery in an Institution A government institution makes decisions regarding certain projects (people’s cases). There are a lot of such projects, and for each project it is known whether it was successful or non-successful. The non-success of projects can be caused by illegally given permits or resources due to bribes. The scenario and the LP-model of the bribe probability are built on the basis of representing the links between civil servants as a graph. The elements of the scenario and the LP-model of bribe probability (risk) are in fact functional departments Z1,…,Zj,…,Zn, each of which consists of Nj civil servants making decisions. In the general case, elements Z1,…,Zj, …, Zn are connected by logical links OR, AND, NOT and there can be cycles. Officials in j-department Zj1, …, Zjr, …, ZjNj make up an IEG. A civil servant making a decision signs the corresponding document. The construction of the LP-bribery model consists in calculating probabilities Pjr, j=1,2, …,n; r=1,2,…,Nj of officials taking a bribe on the basis of statistics from N successful and nonsuccessful projects. Let us consider the LP-bribe model through the example of the conventional bank. The statistics about the successes of loans is used. Loans failure could be explained by bribery. The scenario and the LP-model of bribe probability depend on the structure of the bank departments and their links. The structure could be different, but to be more precise let us accept the structure of the risk model of “the bridge” type, shown in Fig. 13. The object has five elements, which correspond to logical variables Z1, Z2, Z3, Z4, Z5, i.e. functional groups of civil servants, which make decisions about granting loans. For example, civil servants from Z1 and Z2 check loan collateral, while officials from Z3 and Z4 take a decision about the size and the terms of the loan. Officials (bosses) from Z5 control the process. A client approaches one of the bosses, gives him a bribe and is sent to one of the civil servants from group Z3 or Z4, which takes a bribe. The number of civil servants in a group equals the number of grades in a sign. The logical model (L-model) of bribery probability: Y= Z1Z2 › Z2Z4 › Z1Z5Z4 › Z2Z5Z3.

(76)

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The probabilistic model (P-polynomial) of bribes, obtained after the orthogonalization of the logical function (73): P= p2p4 + p1P3 + q1p2p3q4p5 + p1q2q3p4p5 – p1p2p3p4. (77) The given loans turned out to be successful (grade 1) or unsuccessful (grade 0). The provision of loans is proved by documents signed by civil servants, and as a result the loan can be successful or it can fail.

Z1

Z2

1 2 3 1 2 3 4

Z3 Z5 1 2

Z4

1 2 3 4 1 2 3

Y 1 2 3 4

Fig.13. The structural model of the bribe of the “bridge” type

Example. For training P-bribe models, statistics about 1000 loans were used: 700 were good and 300 bad, i.e. average bribery is Pav=300/1000=0,3. Five signs have from 4 to 11 grades; 40 grades in total. As a result of the training, probabilities Pjr and P1jr for all eventsgrades have been determined and the characteristics of LP-bribe models have been calculated: the value of the objective function as a result of training Fmax=720 and the admissible risk value Pad=0.3094. Although probabilities P2jr and P1jr of grades add up to 1 in IEG, they are significantly different from each other (table 12). The probabilities of civil servants’ bribes (probabilities Pjr) differ more than tenfold. The highest average probabilities Pjm (Tables 12 and 13) have eventssigns 1 and 4. The same events make the greatest contributions in average risk Pm. The probabilities of events-signs Pjm differ nearly twofold.

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Table 12. Average probabilities of bribes for groups of officials Group, j

Probabilities, Pjm

1 2 3 4 5

0.478113 0.348310 0.298833 0.388857 0.291868

Probabilities, P1jm 0.249540 0.075949 0.133823 0.116348 0.091775

Number of Officials, Nj 4 10 5 11 10

Table 13. The probabilities of officials' bribes Numbers of gradations Group Z1 1 2 3 4 Group Z2 1 2 3 4 5 6 7 8 9 10

Probabilities, P1r

Probabilities, P11r

Frequencies, P21r

1.0 0.596084 0.248278 0.070927

0.522300 0.311103 0.129579 0.037017

0.274 0.269 0.063 0.394

0.0 0.687703 0.227359 1.0 0.510577 0.704722 0.570149 0.448856 0.434821 0.001675

0.0 0.149933 0.0495688 0.218209 0.111316 0.153643 0.124304 0.097859 0.094799 0.000365

0.0 0.014 0.002 0.054 0.017 0.086 0.057 0.224 0.187 0.359

2.3.4. LP-model to Counter Bribery in the Behavior of Officials Bribery is a crime which people try to conceal. We do not doubt that a crime has happened when, say, a bank is robbed, when clients and clerks are witnesses. A bribe is different from other crimes because it is difficult to ascertain the fact of the crime. However, bribery is a usual phenomenon; there are a lot of data about bribes in judicial and supervisory agencies.

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For each bribe type one could define the signs [37, 38] associated with this crime. Each sign has at least two grades. A P-model of bribe probability (risk) can be trained by statistical data. The investigation of a bribe must be conducted only when the probability of the bribe actually taking place is quite high. Bribe probability can be estimated quantitatively. The following factors are important for the probability of a bribe, taken by a civil servant (a doctor, a teacher): x Age; x Length of service in an office or a company; x The recent purchase of an expensive house, country cottage or a car; x Debts; x Financial requests; x Gambling addiction; x Unusual or extravagant lifestyle; x Unusual behavior; x Complaints; x Vague or criminal past; x Dishonest or immoral behavior at work; x Lack of duties separation; x Lack of independent inspections; x Lack of necessary authority; x Lack of necessary documents and records; x Neglect of existing rules; x Improper document flow system, etc. The above mentioned signs Z1,…, Zj,…,.Zn, each of which has several grades, are the elements of the scenario and the LP-bribe model. Grades for j-signs Zj1,…, Zjr,...,ZjNj make up an IEG. The scenario of a civil servant’s bribe can be described in the following way: a bribe occurs if an event-sign takes place, or any two event-signs take place, or …… all events-signs. The construction of an LP-bribery model consists in calculating the probability Pjr, j=1,2,…, n; r=1,2, …,Nj of a public servant taking the bribe, using the statistics (a set) of bribery facts, established by the court. The L-function (LP-model) of the bribe [38]: Y Z1 2  ... (78) j n.

›z › ›z › ›z

The L-function of bribery risk in the equivalent form after the orthogonalization of (78):

Logical and Probabilistic Management of Socioeconomic Safety

Y

Z1 › Z 2 Z1 › Z 3 Z 2 Z 1 › ....,

101

(79)

The P-function (model, polynomial) of the bribe

P

p1  p 2q1  p3q1q 2  ...

(80)

where the line above the logical variable denotes logical negation. “The arithmetic” in P- bribe models is such that for the final event the value of bribe probability lies within [0, 1] at any values of the probabilities of IE. For each event-grade in IEG the value of bribe probability lies within [0, 1] at any values of the probabilities of IE. For each event-grade in IEG three earlier introduced probabilities P2jr , P1jr , Pjr are used. The biggest number of different bribes equals: N max N1 ˜ N 2 ˜ ... ˜ N j ˜ ... ˜ N n , (81) where N1, …, Nj, …, Nn is the number of grades in events-signs. If the number of signs equals n=20 and each sign has Nj=5 grades, then the number of different bribes equals an extremely big number Nmax=520, which explains the difficulties of counteraction to bribery and corruption. The LP-bribe model (79 – 81) describes all possible bribes and is the most complete and accurate one. However, in some cases we do not have to take into account all possible bribes. For example, it is known from statistical data that a bribe took place when one or two events from Z1, Z2,…,Zn appeared. In order to simplify the models we have to use the Lrisk model with the limited number of different bribes [13]. Example. There were no actual data about bribes which were established by criminal courts. Model data were used as statistical data. There were 1000 people suspected of bribery. Criminal cases were opened against them, but only 300 were found guilty and 700 – innocent. Thus, the average bribery risk equals Pav=300/1000=0.3. The suspects were described by n=20 signs, which had 94 grades in total The identification of P-bribe models (80) consists in finding probability Pjr, r=1,2,…, Nj; j=1,2, …, n of events-grades. At the optimization step the bribe probability is calculated for each suspect and then compared with admissible probability Pad . A suspect is classified as a good one or a bad one. The objective function was formulated as follows: the number of correctly classified suspects must be maximum. Let us discuss the contributions of events-grades in the accuracy of the LP-bribe model using the sample events-grades (Table 14) of signs Z2 and Z13 for the optimally trained LP-bribe model Fmax=826. Table 14 gives the

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frequencies of grades for all P2jr, bad P20jr and good P21jr suspects; the probabilities of events-grades P1jr and Pjr; recognition errors by grades for all Ejr , bad E0jr and good E1jr suspects. The contributions of events-signs in the probability of the suspect’s bribe are proportionate to probabilities Pj, j=1,2,…, n, which are equal to the probabilities of events-grades Pjr. Probabilities Pjr of events-grades of signs differ more than tenfold. Errors of grades Ejr in the bribes classification differ more than fivefold. The LP-analysis of bribes models was conducted using expressions (39 – 42). For each j-sign the following things were defined (Table 15): the average values of probabilities of P1jm and Pjm, ɚs well as the decrease in the number of recognized good and bad suspects Fj when this sign was excluded from the risk model. The LP-model of bribes was trained after this change. The decrease in the number of recognized suspects was defined relative to the optimally trained bribery model with all signs. Events-signs Z1, Z2, Z4 , Z5 , Z6 , Z3 , Z13 make the greatest contribution in the accuracy of recognition. Events-signs Z11 , Z12, Z17, Z18, Z19 make zero contribution. The exclusion of signs 11, 12, 17, 18 decreases the number of recognized suspects only by 4. Table 14. Probabilities and recognition errors for gradations of features P2jr P20jr Sign Z2 0.014 0.007 0.002 0.001 0.054 0.032 0.017 0.005 0.086 0.038 0.057 0.019 0.224 0.066 0.167 0.056 0.359 0.076 Sign Z13 0.019 0.080 0.511 0.142 0.248 0.065 0.028 0.007 0.023 0.006

P21jr

P1jr

Pjr

Ejr

E1jr

E0je

0.007 0.001 0.022 0.012 0.048 0.038 0.158 0.131 0.283

0.010 0.070 0.194 0.159 0.145 0.095 0.067 0.053 0.016

0.019 0.014 0.038 0.031 0.028 0.019 0.013 0.010 0.003

0.214 0.500 0.278 0.412 0.256 0.228 0.169 0.203 0.114

0.429 1.0 0.682 0.5 0.417 0.289 0.196 0.183 0.081

0.0 0.0 0.0 0.2 0.053 0.105 0.106 0.250 0.237

0.110 0.369 0.183 0.021 0.017

0.283 0.233 0.093 0.346 0.044

0.027 0.021 0.008 0.032 0.004

0.237 0.186 0.113 0.178 0.217

0.345 0.201 0.082 0.238 0.117

0.087 0.148 0.200 0.0 0.5

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The accuracy of LP-bribery models changes as the number of grades in the sign is altered. We have conducted research for sign Z2, which in the initial variant has 10 grades. After retraining bribe models the following results were obtained: when there is no sign Fmax=800; when there are two grades in the sign Fmax=808; when there are four grades in the sign Fmax=812; when there are ten grades in the sign Fmax=824; when there are a hundred grades in the sign (at the same time there are seventy empty grades, which are not used for describing suspects in statistics) Fmax=828. The graphs of bribery probabilities per 1000 suspects were built before and after they were sorted according to the probability measure. About 15 % of suspects had low bribe probabilities, i.e. they were very good, and 15 % of suspects had high bribe probabilities, i.e. they were very bad. Therefore, we should divide the suspects according to the degree of bribe probability not into two, but into four or more classes. Table 15. Contributions of parameters to the accuracy of bribe risk models Parameters, j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The number of gradations, Nj 4 10 5 11 10 5 5 4 4 3 4 4 5 3 3 4 4 2 2 2

P1jm

Pjm

' Fj

0.272384 0.063346 0.098475 0.090820 0.080377 0.272148 0.206945 0.266619 0.183897 0.318015 0.251871 0.247375 0.206718 0.235637 0.261648 0.341959 0.289853 0.482499 0.508613 0.750896

0.020226 0.012359 0.009327 0.020927 0.017593 0.022466 0.018549 0.017736 0.014253 0.018295 0.018974 0.017166 0.018900 0.014733 0.017591 0.021975 0.018739 0.017417 0.018138 0.018326

-64 -27 -18 -26 -20 -20 -6 -6 -10 -10 0 0 -16 -2 -8 -2 0 0 0 -2

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2.3.5. LP-model to Counter Bribery based on Analysis of Service Parameters Let us assess a bribe probability using the service parameter statistics, for example the time of solving a client’s problem by a civil servant (government institution) from the moment of filing an application till the final solution of the problem, or the time of denture treatment by a denturist from beginning to end, etc. Such statistics must contain enough service cases to build a discrete or an analytical distribution function. Let there be statistics about service time Yi, i=1,2,…, N for N clients. The approximation of the service time distribution is conducted by the Weibull law with the highest intensity of bribes in the beginning of the process (Fig. 14). 0.3

P

0.25 0.2 0.15 0.1 0.05 0

1-15 16-30 31-45 46-60 61-75 76-90 1

2

3

4

5

6

91105

106120

121135

136150

151165

7

8

9

10

11

Fig. 14. Service time distribution in days (by Weibull law): solid line = real data; dashed line = simulation data

A service parameter can have continuous or discrete values. In both cases, with the aim of increasing the bribe model adequacy and using LPcalculus tools, let us build a discrete distribution at the selected intervals of the partition of parameter values. A grade number is assigned to each interval with the average value of the parameter in it. The grades constitute an incompatible events group (IEG). The probabilities of events-grades are defined by the formula

Logical and Probabilistic Management of Socioeconomic Safety

Pj

N j / N,

105

(82)

The service parameter has average value Ym and admissible value Yad. Let us give the name of bribery risk to the probability P(Y 0) = Ri

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be called risk and denoted Ri. The factors are normalized and lie in the interval [0, 1], therefore the risk value equals the factor value Ri qi . (83) The LP-risk model not taking into account corruption. Counter narcotic actions are usually taken by: x Regional executive authorities (including public health authorities); x Regional departments of federal authorities (Federal Drug Control Service - FDCS, Ministry of Internal Affairs, Prosecution service, Customs office, the Federal Service for Execution and Punishment, etc.); x Non-governmental and religious organizations; x Scientists; x Public opinion. We propose a technique for the assessment and analysis of the risk of the failure to solve a difficult problem “Counteraction to drug addiction in the region”. The hybrid LP-risk model of the failure to solve the drug addiction problem is used, which combines risk scenarios for subjects and objects. The failure to solve a difficult problem DPnar depends on the subjects Snar(S1,S2…,S11), taking part in the solution to the problem, and objects – tasks Tnar(TN1,…,TN6), constituting the core the problem (Fig. 15, left part). The subjects are solving the problem, and the objects are the tasks that are solved in the problem DPnar. The subjects solve the problem, but “the objects” remain- what kinds of problems are solved in DPnar problem? The following subjects are analyzed: S1 – The President, S2 – The Government, S3 – The State Duma, S4 – the Federation Council; S5 – The Prosecutor’s Office, S6 –The Federal Drug Control Service, S7 – The Federal Customs Service, S8 – The Federal Security Service; S9 – Public Health and Social Development Authorities, S10 – Scientists, S11 – Public opinion. The objects-tasks (tasks) are components Tnar: TN1 – the system monitoring the drug abuse situation in the region, ɌN2 – the hybrid LP-risk model of the failure to solve the problem of drug addiction, ɌN3 – the methods of comparing drug abuse in different regions, ɌN4 – the LP-risk model of the conceptual development of drug addiction, ɌN5 – the LP-drug addiction risk model based on indicative factors, ɌN6 – methods of LPanalysis and risk management. Let us denote DPnar, Snar, Tnar, S1, S2,…,S11, TN1, TN2,…,TN6 as events and corresponding L-variables. The scenario of the failure to solve this

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difficult problem DPnar could be formulated as follows: the failure of event DPnar happens due to the failure of events Snar (subjects) AND (logical) events Tnar (objects-tasks).

Fig. 15. The structural model of the failure risk to solve the drug abuse problem

The logical function of events failure:

DPnar = Snar š Tnar ; S nar = S1 › S2 › ... › S11 ; Tnar = TN1 › TN 2 › ... › TN6 .

(84)

The system of probabilistic functions of events failure:

P ^ DPnar = 0` = P ^Snar = 0` + P ^Tnar = 0` (1  P ^Snar = 0`); (85) P ^Snar = 0` = P ^S1 = 0` + P ^S2 = 0` (1  P ^S1 = 0`) + P ^S3 = 0` (1  P ^S1 = 0`)(1  P ^S2 = 0`) + ...; P ^Tnar = 0` = P ^TN1 = 0` + P ^TN 2 = 0` ( 1  P ^TN1 = 0` )+ P ^TN 3 = 0` (1  P ^TN1 = 0`)(1  P ^TN 2 = 0`) + ...

The scenarios for the subjects of the LP-risk model are written, in which their wishes and possibilities are taken into account. Let us develop scenarios and logical and probabilistic risk models for risk models of objects-tasks. The State S1–S4. It includes the President’s Office, the Government, the State Duma, the Federation Council. Unit S5—S9. It includes the Prosecutor’s Office, the Federal Drug Control Service, etc.

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Scientists S10 created LP-models for counteraction to drug addiction in the regions and counteraction to corruption. Public opinion S11 has wish W11 to solve the drug addiction problem in the country. It realizes its possibilities O11 via opposition, mass media (TV, newspapers), meetings, demonstrations, etc. The objects of the hybrid LP-risk model. The LP-risk models correspond to tasks TN1, TN2,…,TN6. Scenario SCi, L-model LMi and Prisk model PMi. are built for each i-task. Statistical data are used in the solution of the problems. The LP-failure risk model, taking into account corruption. The structural risk model of the failure to counteract drug abuse with an account of counteraction to corruption can be found in Fig. 15 (the left and the right section). It logically combines the LP-model of counteraction to drug abuse and the tasks of counteraction to corruption by subjects S, taking part in the solution of the problem. The left part of the structural scheme is borrowed from the LP-risk model of the failure to counteract corruption Zkor. It contains the following tasks, constituting the core of the problem: ZK1 —creation of the system for monitoring corruption in the subjects ; ZK2 — counteraction to bribery and corruption in a governmental institution; ZK3 — counteraction to theft and fraud of civil servants; ZK4 — counteraction to bribery during service. After that, the L-risk function should be written down, then its orthogonalization be performed and the corresponding P-risk model of the failure to counteract drug addiction be written down. Finally, we must write down the P-function for the generalized model and make the corresponding calculations.

2.4.3. The Conceptual LP-risk Model of Forecasting Drug Addiction in a Region Informal descriptions [23] were used to develop separate scenario conceptual LP-models forecasting the risk of drug addiction growth in the region [20]. We have proposed the conceptual LP-model forecasting the risk of drug addiction development in the region, combining separate LPrisk models. The conceptual LP-model, predicting the risk of each development process, is an L-combination of influencing events-factors, which are not quantitative ones. Let us use expert information to assess the risks of events-statements about drug abuse development [14].

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The conceptual LP-model predicting the risk of each development process could be expressed verbally as follows: drug addiction growth risk occurs EITHER due to any factor, OR due to any two factors, OR due to all factors. 1) The LP-model forecasting drug addiction risk due to moral degradation:

Y1

Z1 › Z 2 › Z 3 › Z 4 › Z 5 ,

where Z1 is poor heredity; Z2 – poor family upbringing; Z3 – a person is not conscious of his disease; Z4 – lack of motivation for productive activities; Z5 – lack of moral and ethical guidelines; › – the operation of logical addition. The probabilistic model predicting the risk of drug abuse development:

P{Y1 } R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 )  ... 2) The LP-model predicting the risk of drug abuse development due to the failure to counteract it:

Y2

Z1 › Z 2 › Z 3 ,

where: Z1 is the inefficiency of law enforcement authorities’ actions aimed at counteracting proliferation and withdrawal of narcotic substances from illegal trafficking; Z2 – inefficiency of drug abuse prevention aimed at developing a kind of resistance to drugs by the population; Z3 – inefficiency of authorities’ actions aimed at improving the socioeconomic situation in the region. The probabilistic model forecasting drug abuse growth risk:

P{Y2 }

R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 ).

3) The LP-model forecasting drug addiction development risk due to the deterioration of the demographic situation:

Y3

Z1 › Z 2 › Z 3 › Z 4 › Z 5 ,

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where Z1 – deterioration of survival conditions in the area during the crisis; Z2 – deterioration of the protection of the area’s vital interests; Z3 – deterioration of internal immunity and external protection from destabilizing factors; Z4 – decrease of competition and stability in the economy; Z5 – deterioration of living conditions and sustainable personality development. The probabilistic model forecasting drug abuse growth risk:

P{Y3 }

R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 )  ...

where Z1 – deterioration of survival conditions in the area during the crisis; Z2 – deterioration of the protection of the area’s vital interests; Z3 – deterioration of internal immunity and external protection from destabilizing factors; Z4 – decrease of competition and stability in the economy; Z5 – deterioration of living conditions and sustainable personality development. 4) The LP-model forecasting the risk of drug addiction development due to narcotic substances’ proliferation:

Y4

Z1 › Z 2 › Z 3 ,

where Z1 – deterioration of the population’s susceptibility to taking narcotics; Z2 – deterioration of counteraction to illicit drug trafficking and withdrawal of narcotic substances; Z3 – deterioration of social, economic and political factors determining the risk group size. The probabilistic model forecasting the risk of drug abuse growth:

P{Y4 }

R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 ).

5) The LP-model forecasting drug addiction risk due to the influence of drugs on society:

Y5

Z1 › Z 2 › Z 3 › Z 4 › Z 5 › Z 6 › Z 7 ,

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where Z1 – the growth of the risk of economic crisis situations in the region leading to redundancies or salary delays, shortage of work places, etc.; Z2 – the growth of risk groups due to the above mentioned processes. These groups contain a lot of potential drug addicts; Z3 –alcoholism and drug abuse development in risk groups; Z4 – groups risk growth due to the arrival of the most psychologically vulnerable groups of society – college and university students and minors who live in hostels and orphan asylums; Z5 – decrease in the numbers of youth; Z6 – decrease of workforce in the economy; fall in the production of goods in the area; Z7 – replacement of locals with migrant workers The probabilistic model forecasting drug abuse growth risk:

P{Y5 }

R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 )  ...

6) The LP-model forecasting the risk of drug addiction growth due to the risk of trying drugs for the first time:

Y6

Z1 › Z 2 › Z 3 ,

where Z1 – psychological readiness growth; Z2 – drug availability in the area; Z3 – increase of unsolved crimes of this type; Z11 – a person’s psychological readiness growth; Z12 – psychological readiness growth (support of the environment); Z111 – escaping a hard real-life situation; Z112 – status growth in certain circles; Z113 – no difference is perceived between the notions “to take drugs” and “not to take drugs”; Z121 – lack of career growth perspectives; Z122 – promotion of drugs and the way of life of drug addicts; Z123 – lack of administrative measures; Z124 – availability of drugs and drug dealers in night clubs and similar places. Initiating events Z1, Z2,…,Z124 have no quantitative values. Their risks R1, R2,…,R124 should be evaluated by expert information [14].

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The conceptual L- and P-models forecasting drug addiction growth risk in the region are written down by analogy with the above expressions. The conceptual L-model forecasting the risk of drug addiction in the region is the logical sum of separate conceptual processes Y1,…,Y6: Y Y1 › Y2 › Y3 › Y4 › Y5 › Y6 . (86) The conceptual P-model forecasting the risk of drug addiction in the region:

P{Y } Py1  Py 2 (1  Py1 )  Py 3 (1  Py1 )(1  Py 2 )  ....

(87)

2.4.4. The Fundamental Characteristics of the Drug Situation in the Region The fundamental characteristics determining the state of drug abuse in the region [23] are divided into units B1, B2,…, B7 (Table 16). In column 1 we can find identifiers X1, X2, … of the fundamental characteristics (FC) of the drug abuse situation. Column 3 provides identifiers Y1, Y2, … of indicative factors (IF) of the drug abuse situation, which will be discussed later. The comparison of the drug abuse situation in different regions is conducted by the FC of the drug abuse situation (Table 16). N. V. Hovanov’s method of aggregate randomized factors is used [14]. Let us deal with the characteristics of the regions from the selected unit (Table 17). The last line of the table provides the zero values of characteristics for the ideal region. This table of characteristics is transformed into the factors table. All factors have values in the interval [0, 1]. The software complex provides for setting the signs of the final aggregate factor increase or decrease from the change of characteristics and the nature of the change – linear, convex upwards or downwards. After calculating the factors according to the unit in the table one should exclude the last line for the ideal region Aid and calculate the ratings of the real region A1, A2, …, Am taking account of factors’ weights, as found by expert information. The regions are classified according to each unit of characteristics. Further on, the assessments of regions’ ratings are combined in accordance with units’ weights using NII expert information. The drug addiction situation in the region in accordance with the units is good if it has a low rating and vice versa.

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Table 16. Fundamental characteristics of the drug addiction situation Identif iers FC 1

B1 Y23 X1 X2

X3 X4

X5 X6 X7 X8 X9 X 10 B2

Fundamental characteristics

2

Identifiers II 3 Medical and biological

Primary drug dependency incidence rate per 100 000 people The number of registered drug addicts and abusers per 100 000 people The number of registered drug addicts and abusers per 100 000 teenagers Struck off the register due to death and diagnosis – drug addiction, alcoholic psychosis The number of people poisoned by drugs and psychoactive substances The number of registered drug disorders per 100 000 people The number of deliberate poisoning cases in order to achieve drug intoxication The number of deliberate poisoning cases in order to achieve drug intoxication among minors The number of deliberate poisoning cases in order to achieve alcohol intoxication The number of deliberate poisoning cases in order to achieve alcohol intoxication among minors The level of crime in the illicit drug

trafficking (IDT) area Y24 The number of registered crimes related to illicit drug X 11 trafficking and precursors Including those with intent to sell X 12

X 13 X 14

Recorded crimes committed in the state of intoxication: – alcohol, – drugs, – toxic Identified crimes committed by minors in the state of intoxication: – alcohol, – drugs

Y1 Y2

Y3

Y4

Y5 Y6

Logical and Probabilistic Management of Socioeconomic Safety

X 15

Drugs expropriated, by drug types

X 16

The number of registered serious and very serious crimes in IDT per 100 000 people Synthetic indicative index of level of organized crime

X 17

X 17.1 X 17.2

X 18 X 19

B3

117

Y7

The number of registered crimes related to IDT, Y8 committed in large and extra large sizes, per 100 000 people The number of crimes related to IDT committed by a group of people by prior conspiracy or by an organized group, as part of the criminal cases of crimes for which the investigation is finished, per 100 000 people The number of registered crimes committed by drug addicts or with their participation, per 100 000 people The number of registered administrative offenses Y9 related to IDT, in accordance with the Administrative Code, per 100 000 people Economic costs and damage because of drug addiction

distribution

Y25

X 20

The ratio of addiction social cost to gross product (GP)

Y10

X 21

The ratio of addiction cost to budget expenditure on health and social issues The ratio of addiction cost to budget expenditure on the prevention of addiction Demographic stability

Y11

Level of addiction among female population per 100 000 women Mortality among addicts aged 10–29 per 100 000 people Percentage of minors (10–18 y.o.) in the number of registered addicts The number of registered patients of HIV per 100 000 people The ratio of deceased addicts to newly registered ones

Y13

X 22 B4 Y26

X 23 X 24

X 25 X 26 X 27

Y12

Y14

Y15

118

B5 Y27

Chapter Two

Drug immunity of the territory

X 28

Characteristics of latent component of drug users

Y16

X 29

Development index of human potential

Y17

X 30

Synthetic indicative index "Index of individual development" Feedback

Y18

B6 X 31

X 32 X 33

X 34 X 35 B7

The share of the population who have noticed that there are a lot of drug addicts in their community The share of the population believing that the use of drugs may be harmless to humans The share of the population who are positive about the legalization of "soft" drugs The share of the population who believe that the use of drugs is a private affair The share of the population who have noticed that it is quite easy to get drugs for illicit use in their area Background social statistics

X 36

Population by sex and age groups

X 37

The incidence of main types of diseases among the population Mortality of population by main causes

X 38 X 39

Age-related mortality rates from suicide

X 40

Indexes of economic well-being of the population: the average monthly income per capita, the consumption of foods per capita Distribution of infectious diseases (HIV, hepatitis B, C)

X 41

In Table 16 the synthetic index of the indicative level of organized crime (X17) takes into account: 1) the number of registered crimes related to IDT committed in large and extra large sizes, per 100 000; 2) the number of crimes related to IDT committed by a group of persons by prior agreement or an organized group, as part of the criminal cases of crimes for which the investigation is finished or resolved, for 100 000 people.

Regions (projects, programs) A1 A2 … Am Aid X2

… 0

X1

…

0

0

…

Characteristics X3

Table 17. Classifications of the regions according to the units

… … … … … 0 0

…

Xn

Logical and Probabilistic Management of Socioeconomic Safety

…

Computed values of ratings

119

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Chapter Two

2.4.5. The Indicative LP-model of Danger of the Drug Situation Indicative factors characterize drug abuse danger in the region [20, 23] and define the other aspect of the problem: what must be done? Now we are going to substantiate and propose the LP-risk model of drug addiction in the region by indicative factors. The fundamental characteristics of the drug abuse situation in the region, introduced earlier in Table 16, characterize counteraction measures to IDT proliferation and do not define the risk of drug abuse danger, which can be used to manage the state of drug abuse. One of the main problems is drug abuse latency, namely soft drugs (not from the opium group). The information about the scope of latent crime is represented by the factors of drug addiction latency. Latency assessment in the ITD sphere. Latency factors of ITD are usually assessed by three methods [23]: 1) comparing the data about crime rate and incidence of disease; 2) comparing the data, based on crime rate and public opinion polls; 3) public opinion polls. Now we will give the list of initial factors: A1 – the number of crimes connected with illicit trafficking of drugs. A2 – the number of registered crimes connected with ITD. A3 – the number of current criminal cases connected with ITD. A4 – the number of cases, connected with ITD which were submitted to the court. A5 – the number of solved criminal cases connected with ITD. A6 – the number of administrative offences connected with ITD. A7 – the number of withdrawn narcotic substances. A8 – the number of people diagnosed with drug addiction. A9 – the total population of the area. A10 – the sample volume of the focus group interview. A11 – the share of respondents who have confessed to taking drugs. A12 – the share of respondents who have drug addicts among their friends. A13 – the share of respondents who have noted that they regularly see drug addicts in their neighborhood. A14 – the share of respondents who have noted that they regularly see the traces of drug addicts’ presence in their neighborhood. A15 – the share of respondents who have heard about and are familiar with drug abuse prevention programmes. A16 – the share of respondents who believe that the State’s anti-drug policy must be toughened. A17 – the share of respondents who believe that soft drugs might be legalized.

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A18 – the share of respondents who think that drugs are harmless. A19 – the share of respondents who think that taking drugs is one’s personal business. A20 – the number of people involved in drug abuse prevention programmes. A21 – the number of beds in hospitals where drug addicts are kept. The latency coefficient according to method 1:

K

1 lat

N cal \ N reg ,

(88)

where Ncal – the calculated number of people taking soft drugs; Nreg – the registered number of people taking soft drugs. For methods 2 and 3 latency coefficients are determined by the empirical formulae from [23] in function factors A1, A2,,,,, A21. The intervals of latency coefficients change, based on the values of drug addiction state factors for several years, using methods 1–3, are as follows: Ʉlat1=(8, 56); Ʉlat2 =(14, 30); Ʉlat3 = (47, 62). The final value of the latency coefficient is determined by the formula

K lat

1 3 W1 K lat  W3 K lat ,

(89)

where W1=1/3; W2,3=2/3 – weights of latency coefficients by expert assessment. Indicative factors-events of the drug abuse situation. The fundamental characteristics, for which the notion of the valid event could be introduced, are also the initiating indicative factors which characterize the risk of the drug abuse situation. In Table 16 (column 3) the identifiers of indicative factors are denoted by Y. The links of fundamental characteristics X and indicative factors Y are given in the table (in one line), but are also written in units: B1 : Y1 = X1; Y2 = X2; Y3 = X3; Y4 = X6; B2 : Y5 = X11; Y6 = X12; Y7 = X16; Y8 = X17; Y9 = X19; B3 : Y10 = X20; Y11 = X21; Y12 = X22; B4 : Y13 = X23; Y14 = X24; Y15 = X25; The fundamental characteristics of unit 5 “Drug abuse immunity of the area” were standardized: 1. The index of human potential development Y16 – from the condition that with its increase the risk of drug addiction danger of the area decreases. According to UN reports, which are published every year, the index for the countries changes in the interval [0, 1] (developed countries

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122

have high values). The following formula has been offered for standardization purposes:

Y16

1 /(100 x Y16 ).

(90)

2. The individual development index Y17 – from the condition that with its increase the risk of drug addiction danger risk decreases. The following formula has been offered for standardization purposes:

Y17

1 /(100 x Y17 ).

(91)

3. The latency coefficient Y18 – from the condition that with the decrease of coefficient Klat the risk of drug addiction danger grows [23]. The indicative index of drug abuse latency Y18 = 1 / Klat , where Klat is the latency coefficient from the expression:

Y18

1 / K lat

1 / Y18 .

(92)

The fundamental characteristics of units 6 are 7 are used for calculating the drug abuse latency coefficient in the area Klat and then - the corres7ponding indicative latency factor Y18. The measure of drug abuse danger in the region is risk probability. In the LP-model of risk (probability) of the drug abuse situation in the region, all events have the meaning of danger, which increases with taking into account each new event. In the logical addition of events the system risk (probability) belongs to the interval [0, 1]. Drug abuse danger decreases together with the event’s probability decrease and increases with its increase. Drug abuse always causes damage and losses, so therefore we should talk about risk. However, when we deal with events we talk about their probabilities. Therefore the notions of risk and probability are used as equivalent ones. In LP-models of drug abuse danger in the region the following risks are considered (Table 16): x The risks of the invalidity of events – indicative factors Y; x The risks of the danger of events – units of indicative factors B; x The risks of drug abuse danger in the region by the aggregate of indicative factors Y and their units B; x The risk of drug abuse danger in the region by the aggregate of indicative factors with account of drug abuse latency Y18. The fundamental characteristics Xi , which are constant, are not introduced in the LP-model, because their risk equals 0 and they cannot be

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managed. In the structural risk model (Fig. 15) all edges denote the logical link OR. The arrows from B1, B2,…, B6 go from corresponding indicative factors – events Y. Derivative indicative factors and the LP-model of drug abuse situation risk. The LP-model of drug abuse situation danger risk in the region is built by indicative factors of units B1, B2,…,B6 (Table 16 and Fig. 16). Let us consider these units to be derivative indicative factors-events and logical variables.

Y24

…

Y27

......Y16 Y17

Y18 Y19 Y20 Y21 Y22

Y28

Y29 = B

Y1 Y2 Y3 ..................

Y23

Risk because of drug addiction latency,

Risk because of indicative indexes,

Risk of drug addiction growth in the region, Y30

Chapter Two

Fig. 16. The structural model of danger of the drug addiction situation by indicative indexes

124

Logical and Probabilistic Management of Socioeconomic Safety

125

Indicative factors B1, B2,…,B5, as derivative events, are the functions of corresponding indicative factors Y. The probabilities of the danger of these events lie in the interval [0,1]. The risk of drug abuse danger in the region increases together with the probability growth. The structural model of drug abuse risk based on indicative factors can be found in Fig. 16. The derivatives of indicative factors are defined as the logical risk function from expressions: for the unit – medical biological characteristics:

B1

Y 1› Y2 › Y3 › Y4 ;

Y23

(93)

for the unit – crime rate in the ITD sphere:

B2

Y24

Y 5› Y6 › Y7 › Y8 › Y9 ;

(94)

for the unit – economic cost and damage:

B3

Y25

Y 10 › Y11 › Y12 ;

(95)

for the unit – demographic sustainability:

B4

Y26

Y 13› Y14 › Y 15 ;

(96)

for the unit – resistance to drug abuse in the area:

B5

Y27

Y

16

› Y17 .

(97)

The LP- risk model of drug abuse danger in the region based on derivative indicative factors:

B

Y29

B 1› B2 › B3 › B4 › B5 .

(98)

The LP-risk model of drug abuse danger in the region based on derivative indicative factors with account of drug abuse latency

Y30

Y

28

› Y29 .

(99)

The calculation of latency danger risk. Let us write down the Lfunction of danger risk, caused by drug abuse latency Y28 Y18 › Y19 › Y20 › Y21 › Y22 , (100) where

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Yl8 = 1 / K1lat; Y19 = 1 / K2lat; Y20 = 1 / K3.1lat; Y21 = 1 / K3.2lat; Y22 = 1 / K3.3lat . (101) Using the data from [23] for 2010 the values of coefficients equal: K1lat =56.49; K2lat=14.55; K3.1lat =40.74; K3.2lat=195.4; K3.3lat=170.0 Risks danger from each of the latency coefficients, calculated in accordance with the expressions (92)–(93), equals P(K1lat)=0.017; P(K2lat)=0.071; P(K3.1lat)=0.024; P(K3.2lat)=0.0051; P(K3.3lat) =0.0058. After the orthogonalization of the expression (100) and writing down the Ppolynomial, the final risk of drug abuse latency has been calculated and it equals P(Y18)=0.118389. Its value is more reasonable than according to [23], which is calculated with the introduction of weights for latency coefficients K1lat, K2lat , K3.1lat , K3.2lat, K3.3lat by different methods. Thus, we have introduced derivative indicative factors and logical variables B1 , B2 , B3 , B4, B5, Y28, Y29, Y29 (or derivative risk events) and on their basis we have built the LP-risk model of drug abuse danger in the region (103). The methods of LP-analysis, operational and strategic management of drug abuse risk in the area, as well as the synthesis and analysis of events probabilities in LP-models are described in [12, 13].

2.4.6. Calculations The example is based on the data of monitoring the drug abuse situation in St. Petersburg in 2012. It provides the results of automatized research on the LP-risk model of drug abuse danger by indicative factors as the protocol of calculations in the software complex. The indicative factors are introduced by the numbers of their indexes. The logical function of drug abuse danger risk in the minimal DNF: Y30 = 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 22 + 21 + 20 + 19 + 18, where “+” is the operation of logical addition OR. The probabilistic function of drug abuse danger risk was obtained after the orthogonalization of the logical risk function. The identifiers of indicative factors P and Q=1 – P have the indexes of logical variables. The probabilistic function of drug abuse danger risk in the area: P{Y30}= P17 + P16.Q17 + P15.Q16.Q17 + P14.Q15.Q16.Q17 + P13.Q14.Q15.Q16.Q17 + P12.Q13.Q14.Q15.Q16.Q17

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+ P11.Q12.Q13.Q14.Q15.Q16.Q17 + P10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + P1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17 + Q1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17.P 22 + Q1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17. .P21.Q22 + Q1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16.Q17. .P20.Q21.Q22 + Q1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14.Q15.Q16. .Q17.P19.Q20.Q21.Q22 + Q1.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Q10.Q11.Q12.Q13.Q14. .Q15.Q16.Q17.P18.Q19.Q20.Q21.Q22, where “.”,“+” are the operations of arithmetic multiplication and addition. The probabilities of IE Y1—Y22 have been introduced on the basis of monitoring results (Table 1). Drug abuse danger risk in the region based on indicative factors taking latency into account equals Ɋ(Y30)=0.19185. The risk danger from drug abuse latency alone equals Ɋ(Y28=0.11839). The risks of indicative factors units’ danger are the following: Ɋ{B1}=Ɋ{Y23}=0.028; Ɋ{B2}=Ɋ{Y24}=0.00849; Ɋ{B3}=Ɋ{Y25}=0.01493; Ɋ{B4}= Ɋ{Y26}=0.007449; Ɋ{B5}= Ɋ{Y27}=0.0264; Ɋ{B}= P{Y29}=0.0833.

2.4.7. Conclusion Main results: 1. We have analyzed the methodological support for drug addiction monitoring systems in the region and come to the conclusion that the current models and methods are not adequate for the event and risk.

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2. We have developed the hybrid LP-risk model of the failure to solve the problem of counteraction to drug addiction in the region, as a difficult problem, with scenarios for the subjects taking part in the solution of the problem, and objects-tasks constituting the core of the problem. The models have been developed with and without taking account of corruption. 3. We have developed the scenario conceptual LP-risk model of drug addiction danger in the region, using non-numerical, inaccurate and incomplete expert information. 4. We have developed the LP-risk model of drug abuse danger in the region by indicative factors with account of drug abuse latency as a random event. 5. We have provided the example of calculating the risk of drug abuse danger in St. Petersburg using the monitoring system data, and it has proved the adequacy of proposed risk models for the purposes of assessment and analysis of the drug abuse situation in the area. 6. The proposed LP-models for counteraction to drug addiction in the region will help to reduce the large economic losses from drug addiction in the country and improve the moral environment in society.

2.5. LP-models of Operational Risk and Reserve of Capital under Basel The failures in the banking sector are caused by poor risk management. B.V. Sazykin

The management of the SES under study, belonging to the group SES1 which is of top priority for the State, is aimed at reducing banks’ losses and reducing nearly twofold the value of capital for risk, which, according to the requirements of Basel, constitutes 15 % of a bank’s assets. It is impossible to reduce the losses of banks and clients, to improve quality, to reduce costs, or to develop new banking products without improvement of the bank’s risk management system. Operating risk (OpR) is a kind of banking risk. It causes financial losses and the deterioration of the bank’s reputation. Any banking activity is connected with OpR which affects the work of the whole loan organization and its profits. The peculiarity of OpR is the fact that it is the basis of other risk types. If we study any risk type in detail it will turn out that it can be caused by the human factor, by business

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processes, by system failures or by external factors, which belong to OpR factors [43]. It could be suggested that the higher the ɈpR value is, the more severe the other risks are. Operating risk reflects the protection level of the bank, the qualification of its personnel and its ability to withstand external events. Unlike financial risks, ɈpR appears at first in events: the failure of energy systems, personnel’s mistakes, a flood or a terrorist attack. The elimination of these events or the minimization of their consequences requires a lot of financial resources from the bank. The bank has to plan its actions very carefully in order to avoid bankruptcy in case undesirable consequences follow. ɈpR events tend to accumulate. In the operations of any bank little errors or failures occur every day. If the bank ignores them and does not trace their causes, consequences might follow which could be eliminated only if huge resources were spent. Banks try to conceal ɈpR events in order not to damage their reputation. The problem of identifying and assessing the ɈpR of a bank is very complex. The operating risk of a bank has a complex nature and various sources, and it is difficult to describe formally and simulate. The existing methods of assessing ɈpR are aimed at the solution of separate problems within a single business process of a bank. The determination of risk value within one business process is not always right - we have to take into account its value in its connection with other processes. Operating risks breed market and loan risks [44]. The influence and “interaction” of ɈpR with other risk types might cause big losses and damage the reputation of a bank. The Central Bank of the Russian Federation has made a requirement to loan organizations to create internal procedures and systems which would provide enough capital, corresponding to the size of their businesses, the complexity of their operations and the types of possible risks [45]. The ɈpR assessment system must be integrated in the risk management processes of a loan organization and its results must form an integral part of the process of ɈpR type monitoring. Another important task is the integration of all risk models used in a bank into a general risk assessment model. This would allow owners, partners and other interested people to obtain the integrated risk index of a bank. Basel 3 came into force in Russia on 1 January 2014. It has allowed defining capital requirement more exactly. The introduction of Basel promoted the use of advanced methods for credit risks so far. However, this event prompted the banks to develop and implement their own risk assessment methods. At the same time the Basel Committee itself pays

130

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special attention to the value of ɈpR. Thus, in Basel 3, for capital adequacy assessment it is given the coefficient 12.5 (a similar coefficient is used when market risk is assessed), and not 10 as it used to be. Basel 3 demands a less risky policy from banks, so that they have to find resources for training employees and improving IT-systems, which will reduce both technological and management costs. However, while Basel 3 is being implemented in Russian banks, the ɈpR value is bound to increase.

2.5.1. Logical and Probabilistic Models of Operational Risk of a Bank The model for assessing the OpR of a bank has been built using the classification of operating events proposed by the Basel committee [46]. In the advanced method each business line is analyzed separately. It deals with seven types of unfavorable events of a bank’s OpR: internal fraud Z1; external fraud Z2; recruitment policy and labor safety Z3; clients, products and business practice Z4; physical damage done to assets Z5; violations in business operations and system failures Z6; performance, delivery and management of processes Z7. These are derivative events. Each event from Z1,…, Z7 is divided into elementary definite events, which are called initiating events. Initiating events are considered as independent random events. There are 98 events in total. Each event has its own number; at first numbering is done by IE, and then by derivative events. The final derivative event Y (losses in the business line) has the last number. The number of IE for each business line equals 70 and they have identical names, but their probabilities for each business line are different. Initiating events have probabilities defined by statistical data or by expert information. Each IE corresponds to a logical variable, taking values 1 or 0 (an event will happen or will not happen) with a certain probability. IE probabilities are taken from the statistical data from the previous year of the bank’s operations (Basel recommends a three-year period), or by expertise (in case there is no statistics) [47]. For each business line a structural, a logical and a probabilistic risk model are built. The structural model for one business line. Let us consider the first business line of the bank (Corporate Finance) by way of example. Let us build the structural model and write down the logical risk function for seven types of unfavorable events Z1, Z2,…, Z7 (Fig. 17).

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131

Y1

Z1

Z2

Z3

Z4

Z5

Z6

Z

Fig. 17. The structural model of OpR of the bank in the first business line (Corporate Finance)

The structural model is a risk scenario, which is formulated as follows: event Y1 (losses in the first business line) will happen, if event Z1 OR event Z2, OR Z3, …, OR Z7 happens. In other words, Y1 will happen if at least one of the events from Z1,…, Z7 happens, or if there is any combination of these events, or if they all happen simultaneously (this probability is small, but it differs from zero). The pR logical model for seven types of unfavorable events of operating risk of the bank Z1, Z2,…, Z7 will be written down in the disjunctive normal form as follows:

Y1 = Z1 ∨ Z12 ∨ Z 3 ∨ Z 4 ∨ Z 5 ∨ Z 6 ∨ Z 7 .

(102)

In order to make a transition to the probabilistic risk model, we have to transfer the expression (102) into the orthogonal disjunctive normal form. This transition is not simple; the function dimensionality growth is connected with it. Therefore, here we do not present the results of interim calculations due to their awkwardness. The orthogonalization methods and procedures are described in [46]. After performing these procedures we will obtain the orthogonal L-function, in which L-variables and the signs of L-operations are directly replaced with corresponding probabilities and arithmetic operators. Finally, we obtain the P-model of OpR: P (Y1 = 1) = P ( Z1 ) + P ( Z 2 )(1 − P ( Z1 )) + P ( Z 3 )(1 − P ( Z1 ))(1 − P ( Z 2 )) + ...., (103) The probabilistic risk model in one business line of the bank enables us to calculate the probability of losses in this business line when the probabilities of OpR IE are known. Such models are built in each of 8 business lines in order to calculate the probabilities of events Y1,…,Y8. These models are also used for the

Chapter Two

132

assessment of ɈpR of the bank by the standardized Basel method, using values P(Y1), P(Y2),…, P(Y8) instead of coefficients in the formula of calculating capital for covering losses. The modified formula allows us to define the value of capital for covering losses more accurately, because it takes into account performance peculiarities, unlike aggregate-coefficients for the branch [47]. Let us build the P-model for calculating the ɈpR of the bank. The operating risk of the bank is an L-sum of the probabilities of losses due to OpR events in all eight business lines. The structural model of the OpR of a bank can be found in Fig. 18.

Fig. 18. The structural model of the operating risk of a bank

The logical model of the ɈpR of a bank in the disjunctive normal form looks as follows:

Y1

Y1 › Y2 › Y3 › Y4 › Y5 › Y6 › Y7 › Y8 .

(104)

where: Y – operating risk of the bank; Yi – business line of the bank, i = 1,…,8. By orthogonalizing the L-model we will obtain the P-risk model:

P (Y

1)

P1  P2 (1  P1 )  P3 (1  P1 )(1  P2 )  .....

(105)

In practice we do not have to use the classification of events in accordance with the Basel provisions. LP-models can be adapted for a business line and events types of a definite bank. For example, some Russian banks use the ninth (additional) business line, which reflects events not included in the eight lines mentioned before. The Basel committee recommends including these losses in the line with a bigger profit.

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133

2.5.2. Calculation of Capital to Cover In the general case, when we have to calculate capital for covering the ɈpR of a bank we should, using the statistical data of a bank, calculate probabilities Pi,j,k and losses Li,j,k for each IE Zi,j,k. Here: i = 1,2,…,8 – business line number; j = 1,2,…, – type of events; k =1,2,…, Nj – indexes of IE in j-type of events: Nj = 2 – 20 – the number of IE, referring to type j. The probabilities of IE are calculated from expressions:

Pi , j ,k

Pi , j ,k / N ,

(106)

where Ni,j,k – the number of losses in i-business line due to j-cause from kinitiating event; N – the number of operations in the business line of a bank during the period under study. The assessment of bank capital required for covering ɈpR consists of two parts: expected and unforeseen losses. The reservation sum for expected losses EL is calculated from statistics or could be obtained by summing up all losses for a calendar year (real reservation assessment): 8

EL

7

Nj

¦¦¦ L

i , j ,k

,

(107)

i 1 j 1 k 1

where Li, j .k – total losses due to the realization (or several realizations) of k - event of j - type in i - business line in the accounting period (for example, a calendar year). We propose to assess unforeseen losses ULLP using the formula similar to the calculation of predicted damage for engineering systems [48]:

ULLP

Py Lmax ,

(108)

where PY – the operating risk of the bank; Lmax is the highest possible damage value of the losses for a business line, a particular operation, or for a bank in general depending on the simulation level. A risk manager usually decides which losses must be chosen as L max, depending on the situation. L max could be chosen as the gross profit in a business line, maximum losses in a line or an operation, or L max must be defined on the basis of expert assessments. Capital reservation value for covering risk is calculated according to the formula:

Chapter Two

134

RSub LP

EL  ULLP ,

(109)

Value RsubLP is the lowest reservation limit. The basic method of indicators from Basel 2 and provision 346-ɉ of the Central Bank of the Russian Federation state that reservation for the bank’s ɈpR must be 15 % from the average value of the gross profit of a bank for three years. Making the analysis we also have to know the upper limit of possible losses if the situation develops unfavorably and rare events occur. The assessment of the upper limit of the capital, allocated to ɈpR, is calculated on the basis of the integrated risk probability factor for the whole bank:

RSub LP

Py Q ,

(110)

where: Q – gross profit of the bank; PY – the probability, calculated according to the probabilistic model. Assessments according to (104), (106) and (107) will be different. The choice of the formula depends on the available data and the cost of obtaining these data. Formula (107) assesses the real losses of previous years. Formula (106) shows the lower limit of the capital allocated to the ɈpR of a bank when the losses are known. In practice, it is difficult to give an adequate assessment of losses from a particular event of OpR; therefore it is also necessary to know the upper limit of possible losses. In this case and when the economic and political situation is unstable it is recommended to use formula (110) for calculating the maximum value of reserved capital, using the profit volume of the bank, which could be lost in case of unfavorable events. The choice of formula depends on the situation in the market and it is the risk manager who is responsible for it.

2.5.3. Integration of Models The advantage of the LP-model of ɈpR consists in the possibility of combining it with other LP-risk models. It could give us a chance to build a complex model for calculating the integrated risk factor of the bank. In the activities of any banks there are events which influence several risks at once. Let us call these events “repeated”. The losses due to repeated events should be recorded according to the risks they cause. If they influence several risks and for each of these risks there is a reserve for possible losses, then a double count appears. Undoubtedly, if there are several risk owners, each of them must bear responsibility. But, at the same time, we

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have to pay particular attention to these very events. We propose to build the LP-risk model of the bank with repeated events influencing several processes at once. The technique of building the complex LP-risk model of the bank with L-operations OR and AND, combining the LP-model of ɈpR with LP-models of other risks, gives us an opportunity to perform the quantitative assessment of the bank risk and identify repeated elements which influence several risks at once [48]. Operating risk is kind of a reliability factor of a bank. At present, it constitutes about 5 % of all the bank’s risks [49], but its influence on them is significant. Therefore, its assessment is an important task, ɚnd successful ɈpR management can reduce losses from other risks. Let us build the combined LP-model of operating risk (OpR) and credit risks (CrR) with the logical link AND (Fig. 19).

Fig. 19. The combined model of operating and credit risks

In Fig. 19 the following notation is used: OpR – operating risk; CrR – credit risk; 1 – clients, products and business practice; 2 – performance and processes management; 3 –damage to tangible assets; 4 – organizational violations and system failures; 5 –the violation of data transfer processes; 6 – the wrong technique of loan risk assessment; 7 – the wrong assessment of loan portfolio; 8 – the wrong calculation of reserves size; 9 – collateral assessment error; 10 – accident happening to a borrower; 11 – fraud; 12 – the change of economic conditions; 13 – wrong transaction processing; 14 – inaccurate information provided to a client; 15 – banking risks management error. There are 5 types of events for OpR: 1, 2, 3, 4, 5. For credit risk: events 6, 7, 8, 9, 10. Events 11, 12, 13, 14, 15 are repeated for operation and credit risks. In order to simplify calculations event 11 presupposes both external and internal fraud. Using the combined structural model from Fig. 18 let us write out the logical risk model:

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­Y YOpR š YCrR ; ° ®Y (Y1 › Y2 › Y3 › Y4 › Y › Y11 › Y12 › Y13 › Y14 › Y15 ) š ° š(Y › Y › Y › Y › Y › Y › Y › Y › Y › Y ). 6 7 8 9 10 11 12 13 14 15 ¯

(111)

The probabilistic functions, written out separately for operating and credit risks, will be similar to the function (109). The integral risk value could be obtained by multiplying values P(Y OpR=1) and P(Y CrR=1). For analysis purposes let us calculate the probabilities of ɈpR, credit risk and the integrated factor for two risks (Table 18) without taking account of repeated events 11–15. After that we will introduce repeated events one by one, make calculations in accordance with changed probabilistic models and see how the integrated risk has changed. The value of integrated risk change is called the contribution of an event in risk. Table 18 shows IE probabilities. The probabilities of events were obtained from the experts using the aggregate factors method [14], assuming that the ɈpR share in Russian banks is 5 % [49]. The expert assessments, made by the same method, were used for credit risk, taking into account the fact that the average probability of credit risk portfolio of 25 % is satisfactory. The contributions of repeated IE are presented in Table 19. A repeated event makes different contributions to operating and credit risks. At the same time the operating risk from repeated elements has increased by 3.23 percentage points, and credit risk - by 2.7 percentage points. Integrated risk has changed by 3.34 percentage points. The significances of events for the final event are presented in Table 20. The calculations have proved that repeated IE, which are initiating for several risks, have the greatest significance for the final event. The integrated risk factor could be used as the risk index of a bank. On the basis of this factor a bank will be included in a certain “quality and safety” category. The models above are quite simple, but they reflect the nature of the approach, based on the trees of events, logic and the probabilities theory. The logical probabilistic method possesses the necessary flexibility, which allows adapting models to the specific character of a particular bank, not limiting itself to the framework of the events classification suggested by Basel II provisions. For example, [49] describes the model of internal fraud in a bank, and deals with this phenomenon in more detail. This model could be included in model (108) for a more accurate assessment of ɈpR and for calculating the capital for covering risk.

137

Clients, products and business practice Operation and process control Damage of material assets Organizational violations and system failures Data transmission process violation Wrong technique of credit risk estimation Wrong credit portfolio estimation Wrong calculation of capital reservation volume Mistake in guarantee estimation

Event 0.00146 0.0138 0.0015 0.00041 0.022 0.05677 0.051323 0.036733 0.050401

0.0138

0.0015

0.00041

0.022

0.05677

0.051323

0.036733

0.050401

2 variant (1repeated event)

0.00146

1 variant (without repeated events)

0.050401

0.036733

0.051323

0.05677

0.022

0.00041

0.0015

0.0138

0.00146

3 variant (2repeated events)

Table. 18. Results of calculations on model with repeated events

0.050401

0.036733

0.051323

0.05677

0.022

0.00041

0.0015

0.0138

0.00146

4 variant (3repeated events)

0.050401

0.036733

0.051323

0.05677

0.022

0.00041

0.0015

0.0138

0.00146

5 variant (4 repeated events)

0.050401

0.036733

0.051323

0.05677

0.022

0.00041

0.0015

0.0138

0.00146

6 variant (5 repeated events)

This will give investors, credit providers and other interested parties the opportunity to take decisions quickly and to compare banks.

Logical and Probabilistic Management of Socioeconomic Safety

0.016759 0.0191

0.057103 0.210581 0.026519

0.016759

0.0387473 0.195209 0.007563

1.8087 1.5114

1.8674

3.87473 1.95209

0.7563

OR CR Integrated risk

Contribution of event 1 in changing of risk

Risk without repeated events, %

Risk

0.5207

0.5043 0.4222

Contribution of event 2 in changing of risk

0.3948

0.3824 0.3202

Contribution of event 3 in changing of risk

0.023

0.0223 0.0187

Contribution of event 4 in changing of risk

0.06604 0.218063 0.035745

0.4993

0.4837 0.4049

Contribution of event 5 in changing of risk

0.066264 0.218251 0.035977

0.00024

0.00024

0.062195 0.214844 0.031775

0.0041

0.0041

0.0041

3.34

Difference between final result and primary result 3.23537 2.7091

0.071101 0.2223 0.04097

0.00518

0.0054

0.0054

0.0054

0.016759 0.0191

0.0054

0.016759 0.0191

0.016759 0.0191

0.016759 0.0191

Chapter Two

Table 19. The contributions of repeated events in the change of risk

Accident with borrower Fraud Economic situation changes Mistakes in registration of borrower’s application Inaccurate information given to borrower Mistake in management of bank risks OR CR Integrated risk

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Table 20. Significance of events for final event Number of the initiating event 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Significance of the event +1.81595E-01 +1.83867E-01 +1.81602E-01 +1.81404E-01 +1.85409E-01 +3.1944E-02 +3.17609E-02 +3.12798E-02 +3.17300E-02 +3.06444E-02 +9.77704E-01 +9.64237E-01 +9.62978E-01 +9.5926E-01 +9.64023E-01

An obvious advantage is the possibility of OpR analysis (the determination of events making the greatest contribution in losses) and the inclusion of repeated events which make contributions in different risks. The inclusion of repeated events makes the evaluation of the integrated risk of the bank more accurate. The integrated risk can be used for management purposes. The suggested approach is simple, transparent, accessible to most bank employees and does not require significant financial and human resources. But it might be implemented only if a bank system has effective ɈpR monitoring (registration of events). A bank has to develop a clear classification of events (or employ a ready-made Basel II classification) so that this or that IE might be included into a certain type of particular business line. A serious problem in the implementation of LP-methods of assessment and analysis of OpR is the task of motivating bank personnel to register events without fear of errors and blunders. The employees of all departments must register all new events in a timely manner and send this information to the OpR manager who classifies them and puts them in the database. These databases are used for regular retraining of the model (the calculations of IE probabilities), so that it takes into account changes in the environment and internal operating processes and maintains the required accuracy of assessments.

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2.6. Invalidity LP-model for Quality Management of Systems and Products under WTO A developer should not rely on optimistic forecasts of easy development: he has to know that there will be inevitable errors in the project. Robert Stephenson

The management of the SES under study, which belongs to the group of the highest priority for the State — SES-1 — is aimed at increasing the quality of systems and products according to the demands of the World Trade Organization (WTO), and at increasing revenues from industry and business in the world market. Export goods cannot be produced without a quality certificate.

2.6.1. Construction of LP-model of System Invalidity Let us describe the construction of the LP-risk model of SES invalidity using the example of system Y, which might have dangerous states Y1, Y2,…,Y6. Let us denote dangerous states by events and Lvariables with the same identifiers [12, 50]. The probabilities of events have values in the interval [0, 1]. These states can be valid or invalid. The state is caused by invalid parameters Z1, Z2,…, Z11, which have admissible values and can be inadmissible or dangerous, and they are treated as initiating ones for the occurrence of invalid states Y1, Y2,…,Y6. Invalid states Y1, Y2,…,Y6 are caused  by invalid parameters: Y1  Z3, Z8, Z9, Z10; Y2  Z1, Z5, Z6, Z11;  Y3  Z1, Z4, Z5, Z10; Y4  Z2, Z3, Z8, Z5, Z11; Y5  Z4, Z7, Z9, Z10; Y6  Z2, Z6, Z8, Z11. The scenario, for example, of invalid state Y1 looks as follows: the occurrence of invalid state Y1 depends on Z3 Z8 Z9 Z10. Invalid system states initiate (Ÿ ) invalid parameters: Z1 Ÿ Y2,Y3; Z2 Ÿ Y6,Y4; Z3 Ÿ Y1,Y4; Z4 Ÿ Y3,Y5; Z5 Ÿ Y2,Y3,Y4; Z6 Ÿ Y2,Y6; Z7 Ÿ Y5; Z8 Ÿ Y1,Y6; Z9 Ÿ Y1,Y5; Z10 Ÿ Y1,Y3,Y5; Z11 Ÿ Y4,Y2,Y6. Let us use Table 21 to demonstrate the connection of invalid system states with invalid parameters (events), where 1 is the presence of connection and 0 - lack of connection. Using Table 21, let us write down the shortest paths of invalid states (SPIS) for Y1, Y2,…,Y6 (Table 22). The LP-model of system Y invalidity is the disjunction of SPIS.

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Table 21. Connection of system states and their parameters

States Y1 Y2 Y3 Y4 Y5 Y6

Z1 0 1 1 0 0 0

Z2 0 0 0 1 0 1

Z3 1 0 0 1 0 0

Z4 0 0 1 0 1 0

Initiating events Z5 Z6 Z7 Z8 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1

Z9 1 0 0 0 1 0

Z10 1 0 1 0 1 0

Z11 1 0 0 0 1

Table 22. The shortest paths of invalid system states States

The shortest paths of invalid system states Z1Z8Z9Z10 Z3Z5Z6Z11 Z1Z4Z5Z10 Z2Z3Z5Z11 Z4Z7Z9Z10 Z2Z6Z8Z11

1 2 3 4 5 6

The occurrence of the shortest paths of invalid system states can also be written down as sequences where initiating events are defined in brackets by their numbers:

­Y1 °Y ° 2 °°Y3 ® °Y4 °Y5 ° °¯Y6

(3,8,9,10) (1,5,6,11) (1, 4,5,10) (2,3,5,11)

(112)

(4,7,9,10) (2,6,8,11)

Sequences Y1,Y2,…,Y6 are convenient for planning computer research when repeated events and IE change.

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The functional integrity scheme for this system can be found in Fig. 20. Events 18 and 19 are derivative fictitious invalid events, expressing the influence of initiating invalid events. The L-risk model of SES invalid state occurrence

Y1

Y1 › Y2 › Y3 › Y4 › Y5 › Y6 . The P-risk model of SES invalid state occurrence

P{Y } R1  R2 (1  R1 )  R3 (1  R2 )(1  R1 )  ..., where Rn are risks of events Yn , n=1,2,...,6.

Fig. 20. Scheme of functional integrity for system invalidity

(113)

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2.6.2. Description of Invalid Events Let us use capital letters Z to denote IE or logical variables for these parameters, taking the value 0 or 1 depending on whether, as a matter of fact, the values of parameters belong to the tolerance region OmegaZ. There can be several stages of system development. For each stage (mode) its own sets Z, z, OmegaZ are defined. At the stage IE Z are treated as Boolean logical variables, taking values 1 (validity) and 0 (invalidity). In the scenario for the final event Y the logical expressions for derivative events Y1,Y2,Y3,…,Y6, depending on IE Z, are in fact SPIS. Let us use the terms “validity” and “invalidity” of events for the assessment and analysis of systems and processes: initiating events Z, derivative events Y1,Y2,…,Y6 and final events Y. Invalidity Y is considered in the function of IE invalidity. Let us measure the validity and invalidity of final event Y by risk (probabilities) Py=P(Y=0) and Q(y=1) = 1-P(y=1). In the same manner we will measure the invalidity and validity of derivative events Y1,Y2,…,Y6 and initiating events Z by probabilities, for example, P{Zi} =P(Zi=0) and Q{Zi=1}= 1–P{Zi}. When we assess the invalidity of systems and processes we can consider risk invalidity or the probability of system validity, because their sum equals 1. The choice is made on the basis of scenario treatment of the validity or invalidity of the system under study. The L- and P-functions for invalidity will be written down below more often. Derivative invalid events in a system: Y1=0, if a state is invalid; Y1=1, if a state is valid; Y2 =0, if a state is invalid; Y2=1, if a state is valid, etc. The risk of IE invalidity is determined by measurements or calculations. Initiating parameters like L-variables take values 1 or 0. Initiating events are invalid Z1=Z2=…=Z11=0, if the corresponding parameters Z1,…, Z11 are out of their tolerance regions OmegaZ1, OmegaZ2 … OmegaZ11. To sum up, we have described the technique of building and developing the LP- invalidity model for managing the quality of systems and products in accordance with WTO. The assessment of system performance and products (quality certificate) in accordance with WTO requirements will increase industrial and business revenues in the world market by about 30 %. Works [12, 51, 52] provide examples of the efficient use of LPinvalidity models for managing the development tests of an engineering system.

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2.7. LP-models, Monitoring and Management of the Crediting Process in Banks You are doing well if you have enough money to get a bank loan. Russian humor

The management of the SES under study, belonging to the group SES1 which is of top priority for the State, is aimed at decreasing 1.5 – 2.0 times the number of errors in recognition of good and bad loans, and correspondingly a 1.5 – 2.0 times decrease of the bank’s losses, ɚs well as decrease of interest on credit. We propose a technique for monitoring and management of a real crediting process in a bank. We describe the LP-model of credit risk and prove its advantages. We prove the impossibility of creating the training and testing samples with identical frequency of events-grades for the LPrisk model. Our technique includes the following stages: the determination of the minimal volume of statistical data for the training and the signaling samples, the exclusion of some outdated and incorrectly recognized loans in statistical data, the introduction of the signaling group of completed loans, periodic retraining and substitution of the LP-risk model, and crediting process management.

2.7.1. Statement of the Problem Granting loans to private persons and legal bodies is the basic type of bank activity. All banks are different, because they serve different social groups in different cities and regions and companies of different profiles and sizes with various ownership types. Therefore every bank must have its own credit risk model and a system of monitoring and management of the granting of loans. The advantages of LP-credit risk models include their high accuracy, robustness and transparency [33, 53]. LP-credit risk models have high accuracy of recognizing good and bad loans and seven times greater robustness in the classification of loans than other known models. The transparency of credit risk models is manifested in the following ways: in risk loan analysis, in determination of the contributions of parameters and their grades in credit risk of the bank, and in accuracy of loans classification; in the optimization of the quantity of parameters and their grades; in the transparency of the risk scenario and objective function.

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At the same time for LP-credit risk models it is impossible to create the samples for training and testing which would have the identical frequency of successful and failed loans and events-grades in good and bad loans. Let us describe the technique of monitoring and management of a real loan granting process in a bank, a technique which is aimed at the optimization of the whole crediting process. The essence of this technique: 1) determination of the training sample minimum volume; 2) exclusion of some incorrectly recognized and outdated loans; 3) crediting process monitoring; 4) formation of signaling groups from completed loans; 5) creation of the training sample for building a new LP-risk model; 6) replacement of LP-risk models as new signaling groups of loans are created; 7) analysis and management of crediting process in a bank.

2.7.2. The LP-model of Credit Risk Physical persons’ loans are described by up to 20 parameters (Table 23), and each of them has from 2 to 11 grades [12, 53, 54]. Loan parameters and their grades are considered to be random eventsparameters and events-grades. Events-grades of a parameter constitute an incompatible events group. The events with definite probability lead to a loan failure. The scenario of loan failure risk looks as follows: a loan failure happens due to one parameter, any two or all events-parameters. Table 23. Description of the natural person’s credit (application for credit) Number of parameters 0 1 2 3 4 5 6 7 8

Description of parameters Parameter of default Status of existing checking account Duration in months Credit history Purpose Credit amount Savings account/bonds Present employment since Installment rate in percentage of

Symbol Y Z1

Number of grades 2 4

Z2 Z3 Z4 Z5 Z6 Z7 Z8

10 5 11 10 5 5 4

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9 10 11 12 13 14 15 16 17 18 19 20

disposable income Personal status and sex Other debtors/guarantors Present residence since Property Age in years Other installment plans Housing Number of current credits in this bank Job Number of people being liable to provide maintenance for Telephone Foreign worker

Z9 Z10 Z11 Z12 Z13 Z14 Z15 Z16

5 3 4 4 5 3 3 4

Z17 Z18

5 2

Z19 Z20

2 2

L-risk model of loan failure:

Y

Z1 › Z 2 › ... › Z n .

(115)

L-risk model of loan failure in equivalent orthogonal form:

Y

Z 1 › Z 2 Z1 › Z 3 Z 2 Z1 › ....

(116)

P-risk model of loan failure:

P

P1  P2Q1  P3Q1Q2  ...

(117)

where P1,P2,…, are loan failure probabilities in accordance with parameters; Q1=1 – P1, Q2=1 – P2,…. The values of probabilities for events-grades are substituted in the formula (117). Loan risk is in the interval [0,1] with any values of events-grades probabilities.

2.7.3. Identification of LP-models of Credit Risk The identification (training) of the LP-credit risk model is performed by statistical data [55–59] and consists in determining the probabilities of events-grades Pjr, r=1,2,…, Nj; j=1,2,…, n of admissible credit risk Pad and risk Pi, i=1,2,…, of N loans (Fig. 21). The condition Pi > Pad specifies the following loan types: Ngg – good ones according to the LP-model and statistics; Ngb – good ones according to the LP-model and bad ones in

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accordance with statistics; Nbg – bad ones according to the LP-model and good ones according to statistics; Nbb – bad ones according to the LPmodel and statistics. “Good” credits

0

Pmin

“Bad” credits

Pa

Pb

Pad

Pmax

1

Fig. 21. Scheme for credit classification

Fig. 22. The step wise change of the objective function of the probability of two grade-events

Problem setting. The following is given: statistical data about N loans of the bank with Ng good and Nb bad loans and the P-risk model as the system of equations for loans (19). We have to find: probabilities Pjr, r=1,…, Nj; j=1,…, n of events-grades and admissible risk Pad, dividing the credits into good and bad ones. The objective function: the maximum number of loans with the correct classification:

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The objective function: the maximum number of credits with the correct classification: F N bb  N gg o max . (118) From expression (118) it follows that the errors of the LP-risk model in the classification of good Eg and bad Eb loans and on average Em equal (119) E g N gb / N g ; Eb N bg / N b ; E m ( N  F ) / N . Limitations: 1) the probabilities Pjr must satisfy the condition: 0  Pjr  1, r 1,2,..., N j , j 1,2,..., n ;

(120)

2) average credit risks by P-models and statistics must be nearly equal in order to retain the real sense of probabilities; 3) admissible risk Pad is defined to make recognition errors of good and bad loans equal (the recognition asymmetry principle). The identification of P-models has the following peculiarities: 1) the objective function depends on lots of positive parameters Pjr (94 for credit risk of physical persons); 2) the objective function, which equals the number of correctly recognized good and bad loans, has whole values and steps (Fig. 22) in the 94-dimensional space; 3) the objective function has local extremes in the form of flat sites; 4) it is impossible to calculate the derivatives of the objective function F by Pjr analytically; 5) while searching the optimum Fmax we cannot give all Pjr positive or negative increments, because the average risk will change. Training by the Monte Carlo method. During training we determine not the probabilities Pjr, but the relative values of probabilities P1jr of events-grades in the IEG. The connection of probabilities Pjr , P1jr , P2jr in the IEG is performed in accordance with the Bayes formula (26). For calculating the probabilities increments by the random search method the following formula has been proposed:

Logical and Probabilistic Management of Socioeconomic Safety

'P1 jr

K1

N opt  N v N opt

K 3 P1 jr , r 1,2,..., N j , j

149

1,2,..., n , (121)

where Kj=0.05 is the coefficient; Nopt, Nv – the given number of optimizations and the number of the current optimization; K3 – the random number in the interval [-1,+1]. During the optimization process 'Pjr tends to zero. Formula (121) provides a simple setting of initial values and the increments of probabilities, optimization convergence and the determination of the accuracy of assessment of probabilities by their increments in the last optimization. At every optimization step Nmc optimization attempts are made by the Monte Carlo method. If an attempt was successful and the objective function (118) increased, one has to remember the obtained probabilities Pjr and P1jr and continue the optimization process. If all attempts Nmc have failed, the deviation from the target is 2–4 units. The meaning of this is obvious: the objective function is in the local point of extreme (in the step area), therefore the objective function value decreases: F F  'F . (122) During new optimization steps the other values of probabilities will be obtained. Therefore, the optimization trajectory will be beveled and the objective function might increase. The proposed algorithmic iterative method of LP-risk model identification allows its optimization with any complexity level of the LPrisk model and any amount of loans, parameters and grades. Training by the gradient method. Training by the Monte Carlo method is a random non-iterative process. In order to control results using this method a determinate gradient method of training credit risk models by statistical data has been proposed. The following formulae have been proposed for training LP-credit risk models by the determinate gradient method: 1

'P1

jr

2

'P1

jr

K1 P1 jr

N opt  N v N opt

K 2 'P11jr 'F jr ,

,

(123) (124)

where K1 = (0.1–0.15) – the coefficient for calculating the objective function gradient; K2 = (0.2 – 0.3) – the coefficient of changing the

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probabilities step by the objective function gradient; 'Fjr – the objective function increment when only one probability Pjr is changed. The Bayes formula is used during optimization according to formulae (121–124) for the connection of probabilities Pjr and P1jr in the IEG (26). The probabilities P1jr in the IEG are normalized in accordance with the definition (22). Algorithmic iterative methods of the LP-risk model identification allow retrieving new data from the database (the probabilities of eventsgrades and admissible risk) with an LP-risk model of any complexity level and any number of loans in statistics, parameters and grades. The computer research was done using the Western statistical data package consisting of 1000 loans (700 good ones and 300 - bad ones) [54]. The loans were described by n=20 parameters, which had 94 event-grades in total. During identification the function value Fmax=822 was obtained. The LP-credit risk model has far fewer errors in the classification of loans Em=0.15; Eg=0.17, Eb=0.16 than the known methods, which have Fmax=720–750; Em=0.25–0.28.

2.7.4. LP-analysis of Credit Risk For LP-analysis of credit risk the following factors must be calculated [12]: The average probability of events-parameters in the IEG: Nj

¦ P P2

Pjm

jr

jr

, j 1, 2,..., n. .

(125)

r 1

The contributions of events-parameters in the loan risk equal P(i )  P(i ) | p j 0 , j 1,2,..., n .

'Pj

(126)

They are determined by calculating the difference between the state risk value for the optimal model, being the condition of giving the zero value to the corresponding probabilities of grades. The contributions of events-parameters to the average loan risk Pm: 'Pjm Pm  Pm | p j 0 , j 1,2,..., n . (127) Contributions of events-parameters to average risk Pm of credits equal F  F | p j 0 , j 1,2,..., n . (128)

'F j

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The contributions of events-parameters to the function Fmax, i.e. to the LP-model accuracy, is different. Parameters 11, 12, 17, 18 and 19 have zero contributions. They should not be introduced in the LP-risk model of a bank on the basis of these particular statistical data. The contributions of events-grades in the average risk 'Pjm and accuracy of the risk model Delta Fjr cannot be calculated using the expressions of the type (126 – 128), because it is not clear how the frequencies of other grades P2jr in the IEG must be corrected, if one of them is given a zero value. The significance of events-grades is assessed by the errors in the loans classification: g b b m bb E gjr ( N gjr  N gg ( N bjr  N bb ( N jr  N gg jr ) / N jr ; E jr jr ) / N jr ; E jr jr  N jr ) / N jr , (129) where Njrg, Njrb, Njr – the numbers of good, bad and all states with the gradation; Njrgg, Njrbb – the numbers of good, bad and all states with the correct classification of states.

2.7.5. Inability to Create the Testing Samples The general Vcom training Vteach and testing Vtest sample was trained by the identification method. The volumes of the samples were equal 1000 – 700 – 300. Recognition errors of good and bad loans practically coincided during training. There is an erroneous conclusion in [33, 55–57] that the training and testing sample is not needed for assessing the accuracy of the LP-risk model. However, the error in the classification of bad loans while testing according to the classical scheme using the sample Vtest is nearly twice as big. Two different credit risk models have been compared: CART-models on the basis of cluster analysis and LP-models. The comparison of recognition errors while using CART-models and LP-models (Table 24) shows that the LP-model has higher accuracy of recognizing good and bad loans than the CART-model and nearly the same recognition errors while testing. Table 24. Recognition of credits by different models on learning and control CART “Good” credits, Eg “Bad’ credits, Eb

Learning mistakes 0.33 0.28

Test mistakes 0.35 0.23

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LP-model “Good” credits, Eg “Bad” credits, Eb

0.17 0.17

0.30 0.34

For LP-models it is impossible to create samples for training and testing with identical events frequency. Identical samples are such training and testing samples which have the same frequencies of good and bad loans, as well as the same frequencies of events-grades of each eventparameter in good and bad loans. For one event-parameter we can divide credits into identical training and testing samples. However, for any other event-parameter with its own event-grades there will be training and testing samples with other loans. Indeed, training and testing using training and testing samples of equal volume Vteach=Vtest=500 when Ng=350 and Vb=150, which were replaced afterwards, produced the following results (Table 25). In the first and the second variant there are a few nearly identical errors in the classification of good and bad loans during training (columns 2 and 4) while during testing (columns 3 and 5) the number of errors in the classification of good and bad loans is twice as big and they are also practically identical. It proves that it is impossible to create training and testing samples with identical events frequencies. For this reason ɚ task has been set to develop a technique of monitoring and managing the real loan granting process in a bank, which would improve the quality of the whole loan granting process. Table 25. Learning and testing on samples 500-500 and with replacing them with each another

Parameters

1 Eg Eb

Learning on 500 credits 2

Testing on 500 credits 3 Variant 1 0.15 0.29 0.13 0.35

Learning on 500 credits 4

Testing on 500 credits 5 Variant 2 0.16 0.26 0.13 0.36

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2.7.6. Monitoring Technology A technique of monitoring, training LP-models and managing a real credit granting process has been proposed [53]. It has the following features: x the statistical data about the completed loans of a bank is used as a training sample, x the volume of a training sample is limited, x some incorrectly recognized good, bad and outdated loans are excluded, x the signaling group is formed from completed loans, x a training sample is created for building a new LP-risk model, x the old LP-model is replaced with a new LP-credit risk model, x the crediting process is assessed using several factors (criteria). The volume of the training sample. We have done computational research into the effect the volume of the training sample has on the recognition of loans errors. The errors of recognizing good and bad loans grow asymptotically as the sample volume increases (Table 26). The probabilistic model has a limited number of coefficients-probabilities for events-grades. An LP-model can recognize credits better, if there are few of them in statistical data. For training LP-models when there are 20 events-parameters and 94 events-grades we might set the minimum number of loans in a training sample as Nmin=1000–1200: as the number of loans in statistical data grows the number of recognition errors of good and bad loans stays nearly the same. This is an important advantage of an LP- credit risk model. Table 26. Dependence of recognition mistakes on the learning sample volume

Parameter Fmax Eg Eb

1000 826 0.174 0. 173

Learning sample volume 800 600 400 664 508 342 0.171 0.16 0.154 0.167 0.139 0.125

200 182 0.114 0.033

The exclusion of some incorrectly recognized and outdated loans. Credit risk is described by 20 parameters-factors. An LP-model cannot be absolutely accurate, because it takes no account of some other factors due

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to legal proscriptions. Clients could keep money at home (not in a bank) and the bank will not be informed about it. A force majeure event might happen. A client cannot be asked questions about his relations with his wife, mother-in-law, about his health or the health of his family members. This latent information causes the appearance of incorrectly recognized loans. Incorrectly recognized loans should be partially excluded from the DB and the process of retraining LPmodels. The Russian economy is in the process of its development and the information about outdated loans should be gradually excluded from the process of retraining LP-models. Let us study the increase of LP-models’ accuracy in recognizing good and bad loans by excluding some incorrectly recognized loans. For illustration purposes let us use Fig. 23, which gives the calculated distribution of all, good and bad loans after training the LP-risk model by statistical data about loans in a bank. The incorrectly recognized good credits Ngb are in the risk interval [Pad , G] and incorrectly recognized bad objects Nbg – in the interval of risks [B, Pad]. The number of loans in the training sample after excluding some outdated and incorrectly recognized loans:

N

N  a1 N gb  a2 N bg  a3 Nold

* * * N  N bg  N gb  N old ,

(130)

where a1, a2, a3 – coefficients with the values in the interval [0,1]; Ngb*, Nbg*, N*old are the credits excluded from the statistical data base and approximated to integer values. Credits with the greatest risk (i.e. in “the tail” of good loans distribution) are excluded from Ngb (Fig. 23). Credits with the least risk (i.e. in “the tail” of bad loans distribution) are excluded from Nbg. The values of coefficients a1, a2, a3 depend on the loans completed in a bank during a year. We should take values a1, a2, a3 in the interval [0, 1], i.e. move gradually to the optimal accuracy of good and bad loans recognition. Analysis of coefficients a1, a2, a3 could be corrected on the basis of training factors. The results of the calculation research of good and bad loans recognition errors (Table 27) prove that the share of excluded incorrect loans (column 1) changed from 0 bis 100 % from their total number. Columns 2, 3 and 4 show the quantity of all, good and bad loans in the training sample. In columns 5 and 6 we would find the quantity of excluded incorrectly recognized good and bad loans. Column 7 gives the percentage of good and bad loans recognition and columns 8 and 9 – recognition errors of good and bad loans. When incorrectly recognized

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loans are excluded the recognition errors of good and bad loans tend to zero. The signaling group from completed loans. Let us make up a signaling group from the last completed loans with volume Nsign. The signaling group also includes good Ng sign and bad Nb sign loans. The average risk of loans in the signaling group equals Pm sign= Nb sign / Nsign. It is one of the main factors of assessing the quality of the whole credit granting process. The number of loans in the signaling group Nsign=50 – 200 is enough for assessing the credit granting process with acceptable accuracy: average risk loans and the optimality of the process of exclusion of incorrect and outdated loans in statistical data. The final size of the signaling group Nsign is determined taking account of the number of loans, granted and completed by a bank during a year. The periodicity of retraining the LP-credit risk model. The periodicity of retraining the LP-credit risk model is the number of completed loans Nsign in the signaling group. The LP-credit risk model is retrained after accumulating each next signaling group of completed loans. But, in general, the retraining of LP-credit risk models can be conducted as often as bank specialists think it necessary. These specialists take into account the technique of the whole crediting process. good all bad

B Pmin

Pm

G Pad

Fig. 23. Distribution of all, good and bad credits

Pmax

Chapter Two

Overall number of credits, N

2 1000 962 926 888 852 814

Percentage of accepted credits, %

1 0 20 40 60 80 100

3 700 674 649 623 598 572

Good credits Ng

4 300 288 277 265 264 242

Bad credits, Nb

5 0 26 51 77 102 128

Number of accepted good credits 6 0 12 23 35 36 58

Number of accepted bad credits

7 81 84 86 89 91 93

Percentage of recognition

Table 27. Consequent learning with exception of incorrectly recognized credits

156

Mistake in “good” credits, Eg 8 0.183 0.169 0.151 0.13 0.115 0.1

9 0.193 0.163 0.120 0.072 0.0354 0.0

Mistake in “bad” credits, Eb

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The specification of the training sample size. Taking into account the number of loans in the signaling group Nsign, the number of loans in the training sample after the exclusion of some outdated and incorrectly recognized loans equals: N N  N sign  a1 N gb  a 2 N bg  a3 N old , (131)

Taking into account the limitation of the training sample size, let us write down the condition for selecting and correcting exclusion coefficients a1, a2, a3 of outdated and incorrect loans from the training sample:

N sign

a1 N gb  a 2 N bg  a 3 N old .

(132)

2.7.7. Replacement of Risk Models The loan debtors classification using the CART-model. For instance, a bank uses a CART-model of credit risk. The bank would like to replace it with the LP-credit risk model. There are N completed loans in the statistical data, including Ng - good and Nb - bad credits. The average credit risk of the bank equals: Pav N b / N . (133) Special attention must be paid to the fact that N is the number of clients which were acknowledged as good ones by the CART-model and which received loans. If M clients ask for a loan in a bank, the clients’ satisfaction coefficient will equal: Ks N / M . (134) Coefficients Pav and Ks are the success factors of the bank’s credit granting process using the CART-model of credit risk. LP1-model of the bank’s credit risk. The construction of the LP1model of the bank’s credit risk using the identification method was based on the statistical data regarding the CART-model. N1=N good clients including N1g - good and N1b - bad ones are involved in the credit granting process. As a result, for all loans their risks were calculated, the numbers of loans N1gg, N1bb, N1gb, N1bg were determined, and the probabilities of events-grades and admissible credit risk P1ad were assessed. Based on these results, the factors of LP1-risk model success are calculated recognition errors of good and bad loans and in general:

E1g

N 1gb / N 1g ; E1b

1 N bg / N 1b ; E1m

1 ( N bg  N 1gb ) / N 1 . (135)

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The LP-risk model replacement (Fig. 24). The LP1-model during the crediting process classifies the clients into good ones and bad ones. N2 good clients receive their loans. When a time has passed the loan is closed as a good one or a bad one. The completed loans are included in the DB. The last completed loans make up a signaling group of loans. As soon as the signaling group of loans achieves a preset size, the logical condition K starts a procedure which creates a new training sample for building a new LP2-risk model [53]. The new training sample contains the following completed loans: * * * N 2 N  a1 N 1 gb  a 2 N 1bg  a 3 N old  N sign N  N sign  N bg  N gb  N old , (136) where a1, a2, a3 – exclusion coefficients: Ngb*, Nbg*, N*old – outdated credits, excluded from the training sample. After the exclusion of old N*old and incorrectly recognized loans N*gb and N*bg and adding loans from the testing group Nsign a new LP2- credit risk model is built (trained) using the identification method. As a result all loans had their risks calculated, the numbers of loans were defined N2gg, N2bb, N2gb, N2bg, the probabilities of events-grades were assessed, as well as admissible P2ad and average P2m credit risks.

Fig. 24. The scheme of crediting process monitoring and LP-risk model replacement

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160

The following factors of LP2-risk model success are calculated: x recognition errors of good and bad loans and on average: 2 N gb / N 2 g ; E2 b

E2 g x

N bg2 / N 2b ; E2 m

2 ( N bg2  N gb ) / N2.

(137)

the average credit risk in the signaling group of loans and the average credit risk for the whole statistical data sample, the clients’ satisfaction coefficient.

Further on, the LP1-model is replaced with the LP2-risk model and the monitoring system is started, while continuing to serve new clients. The credit granting process in a bank is monitored discretely as the signaling groups Nt sign, t=1,2,…. are created from completed loans. After each signaling group the new LP-model of credit risk is built, thus replacing the old LP-model.

2.7.8. Management of Crediting Process The aim of crediting process management is an increase of the accuracy of recognizing bad and good loans and, consequently, a decrease of the bank’s losses. For management purposes the factors (criteria) of the whole crediting process in the bank are determined by [53]: 1. The bank clients’ satisfaction coefficient:

K st

Nt / M t,

(138)

where M t is the number of loan applications; Nt – the number good clients, who were granted loans. 2. The average credit risk of the bank on the basis of completed loans:

Pavt

Ybt / Y t ,

(139)

where Yt is the number of completed loans, including Ytg – the number of good loans; Ytb – the number of bad (troublesome) loans. 3. The average credit risk of the signaling group:

Pavt sign

t N bt sign / N sign .

(140)

For the purposes of managing the crediting process a training sample for a new LP-risk model is created, the LP-credit risk model is trained; the old LP-risk model is replaced with the new LP-risk model. Crediting

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process management is conducted according to monitoring results and consists in calculating the following parameters: x the size of the signaling group of loans and the periodicity of training and the replacement of models; x the recognition errors of good and bad loans and on average; x the average credit risk in the signaling group of loans; x the average credit risk for the whole sample of statistical data; x the clients’ satisfaction coefficient; x exclusion of coefficients a1, a2, a3 – incorrectly recognized good and bad loans and outdated loans. The management of the credit risk LP-model is performed according to the results of its training and analysis of the contributions of eventsgrades: x the client’s credit risk, which is compared with admissible risk and then a decision to grant a loan is taken; x the coefficient of good and bad loans recognition asymmetry; x recognition errors of good and bad loans and on average; x credit cost, depending on loan risk and its difference from admissible risk; x the number of parameters describing a loan. The software. The procedures of the credit granting process, including the identification of the LP-credit risk model, monitoring, calculation and analysis of factors and management, have a high computational complexity and cannot be performed without special software. This software has been developed by us and it will be described in Chapter 3. It is also used by students when they do laboratory work. The following conclusions have been made on the basis of the research into the development of the LP-credit risk model, monitoring and management of the credit granting process in the bank: 1. We have determined the advantages of the LP-credit risk model: high accuracy, robustness and transparency, as well as the solution of the problems of loan risk analysis and management. 2. We have proved that it is impossible to create the events-grades of training and testing the samples for the LP-risk model with the same frequency. 3. We have presented the data about the LP-credit risk model, its identification and credit risk analysis. 4. We have proposed a technique of monitoring and management of a real credit granting process in a bank: determined the structure and

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the size of the training sample and the signaling group of completed loans; we have also proposed the rules of exclusion of outdated and incorrectly recognized loans and the periodicity of the LP-risk model replacement. 5. The monitoring and management technology contains the following new approaches: x the creation of the signaling group from completed loans; x the creation of the training sample for building the new LP-risk model from the completed loans of the bank excluding some incorrectly recognized good, bad and outdated loans; x the replacement of the old LP-model with the new LP-credit risk model while signaling groups with completed loans are being created; x the assessment of the factors of the whole credit granting technology quality: bank clients’ satisfaction coefficient, the average loan risk of the bank based on completed loans, the average risk of the signaling group of completed loans, eventsgrades probabilities, admissible credit risk; recognition accuracy of good and bad loans and on average. 6. The management of the quality of the whole credit granting process in the bank is performed through the change of parameters of the LP-risk model and monitoring technologies. The proposed technique of monitoring and management of the real credit granting process will make it possible to reduce 1.5 times recognition errors of good and bad loans and reduce bank losses correspondingly, to reduce interest on credit and increase crediting efficiency.

2.8. LP-management of Risk and Efficiency of the Restaurant “Prestige” The true logic of our world is the estimation of probabilities. D. K. Maxwell

The management of the SES belonging to the group of local SES-3 for companies and firms depends basically on their wishes and possibilities. We have performed a detailed analysis of risk efficiency based on the statistical data of a real restaurant. LP-approach to analysis and management can be used for managing risk and efficiency of shops and

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warehouses, whose daily goods turnover also depends on the day of the week, season, advertisement, staff and goods. The SES of LP-management of risk and efficiency of a restaurant uses the LP-risk models of “LP-efficiency” and “LP-classification” classes. The restaurant’s LP-risk and efficiency model is built and analyzed using the monitoring data - daily registration of goods turnover. The restaurant business is described in many works [60, 61]. The present research was done using the statistical data from a real restaurant [13]. The restaurant’s state is determined by the efficiency parameter Y and initiating parameters Z. Parameters Z can be quantitative and qualitative, and can vary in nature and dimensionality. Parameters Z and Y are considered as random variables. We will discuss the problems of analysis and management of the restaurant's risk efficiency using the contributions of parameters Z to the efficiency parameter Y.

2.8.1. Initiating Parameters and their Graduations The efficiency parameter (goods turnover during one day) Y is treated as a random value depending on parameters Z. Parameters Z are represented by the sets of discrete values, which are called events-grades and denoted by L-variables. The statistics for the calendar year were studied (N = 365 days). The restaurant’s state is determined by the following parameters and their grades: Z1 – month, grades: 1, 2, …, 12; Z2 – day of the week, grades: 1, 2,…,7; Z3 – type of advertisements: 1 – for months 3,…,8; 2 – for months 9,…, 12; Z4 – a team type is determined by its staff and depends on the season and days of the week: 1 – for months 9, …, 12; 1, 2 on days 1, 2, 3, 4; 2 – for months 9, 10, 11, 12, 1, 2 on days 5, 6, 7; 3 – for months 3, 4, 5, 6, 7 on days 1, 2, 3, 4; 4 – for months 3, 4, 5, 6, 7, 8 on days 5, 6, 7; Z5 – staff qualification: 1 – inexperienced (2. 2006 – for months 11, 12), 2 – average qualification (2007 – for months 1, 2, 3), 3 experienced (2007 – for months 4,…,10); Z6 – type of menu: 1 – for 2006, months 11, 12 (70 % usual plus 30 % Gourmet); 2 – for 2007, months 1, 2 (65 + 35 %); 3 – for 2007, months 3, 4 and 5 (60 + 40 %); 4 - for 2007, months 6, 7, 8 (55 + 45 %); 5 – for 2007, months 9, 10 (50 + 50 %);

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Z7 – type of event: 1 – usual; 2 – usual plus a banquet; 3 – usual plus a thematic one; 4 – usual plus tasting; Y1 – goods turnover of the restaurant by two grades: 1 – good, 0 – bad. Y2 – goods turnover of the restaurant by the intervals. The grades of the goods turnover Y were obtained by dividing the range of goods turnover by days (thousands of rubles) into the intervals of 25 000 rubles. 1,2,…, Ny=23 of events grades were obtained. The restaurant states were monitored during the calendar year (N=365 days). Every interval had N/Ny=365/23=16 restaurant states on average. The last three intervals are wider than the others. Thus, for the goods turnover Y the following grades were introduced: 1 – [1 – 25]; 2 – [26 – 50]; 3 – [51 – 75]; 4 – [76 –100]; 5 – [101 – 125]; 6 – [126 – 150]; 7 – [151 – 175]; 8 – [176 – 200], 9 – [201 –225], 10 – [226 – 250], 11 – [251– 275], 12 – [276-300], 13 – [301 – 325], 14 – [326 – 350], 15 – [351 – 375], 16 – [376 – 400], 17 – [401 – 425], 18 – [426 – 450], 19 – [451 – 475], 20 – [476 – 500], 21 – [501 – 600], 22 – [601 – 700], 23 – [701 – 1400].

2.8.2. Database and Knowledge Base about States of the Restaurant The restaurant’s states by days are put together in the DB and the KB (Table 28). A system of LP-failure risk functions (18 – 19), which form the knowledge base, is written down. The monitoring of the restaurant’s state and its goods turnover was performed by days (Fig. 25 and Table 28). In October 2006: goods turnover – 1860 thousand rubles, the average daily goods turnover – 60 thousand rubles; minimum – 38 thousand rubles; maximum – 96 thousand rubles. In October 2007: goods turnover – 7340 thousand rubles; the average goods turnover – 237 thousand rubles; minimum – 124 thousand rubles; maximum – 450 thousand rubles. In October 2007 the average daily goods turnover without an entertainment programme (banquets, etc.) amounted to 174 thousand rubles. The entertainment programme increased the average daily goods turnover by 63 thousand rubles. Banquets (weddings) increase the goods turnover significantly. At the same time thematic and tasting events increase the goods turnover insignificantly, by 15 – 20 thousand rubles, but they play a major role in advertising the restaurant.

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Fig. 25. Turnover of the restaurant by days in October 2006 and 2007

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3 4 5 6 7 1 2

11 11 11 11 11 11 11

Z1

Day of the week, Z2

Month

2 2 2 2 2 2 2

Type of advertising, Z3

1 1 2 2 2 1 1

Type of the team, Z4

1 1 1 1 1 1 1

Z6

Z5

1 1 1 1 1 1 1

Type of menu,

Quality of staff, Z7

1 1 1 1 1 1 1

Type of evening,

3 3 6 6 3 3 3

Turnover, gradations Y1

Table 28. A fragment of the tabular knowledge base with regard to the conditions of the restaurant

166

56 54 128 150 68 54 56

Turnover, Thous. rubles. Y2

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2.8.3. Frequency Analysis of Risk and Efficiency Frequency analysis of failure and efficiency risk of the restaurant consists in determining probabilities P2jr, j=1,…, n; r=1,…,Nj. A minimum admissible value Yad is set and the frequencies of grades in “the tail” of efficiency parameter Y distribution is determined (Fig.26). Management is conducted using the values of the frequencies of grades in “the tail” of the efficiency parameter distribution. The goods turnover distribution histogram follows not the normal law, but, rather, the Weibull law with the highest intensity in the beginning. The contributions of events-grades in the restaurant’s risk were calculated under the condition Y < Yad for three variants Yad = 75; 100; 125 thousand rubles. For Yad = 125 thousand rubles the results can be found in Table 28. The following conclusions were made on the basis of the contributions of grades parameters Z1, Z2,…, Z7: x the admissible goods turnover Yad and Risk grow simultaneously, x as the admissible goods turnover Yad grows, the probabilities of events-grades Pjr tend to the average value in the IEG – Pjm, x the admissible restaurant failure risk when Yad =125 thousand rubles is quite high, Risk = 0.37. The goods turnover of the restaurant for three days should not be less than 125 · 3 =375 thousand rubles. The risk of this event is high: Risk = 0.37 · 0.37 · 0.37 =0.051. The analysis of probabilities of events-grades of parameters Z1, Z2, …, Z7 when Yad =125 thous. rubles with Nad =136 and Risk = 0.3726 (Table 29) allows making solutions regarding the management of the restaurant’s risk and efficiency.

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Fig. 26. The histogram of the goods turnover distribution

Z1 – months: the largest contributions to risk were made by the first months of the restaurant’s work: November, December, January, February and March when the staff were still inexperienced and not the best menu types were used. Z2 – days of the week: the largest contributions to risk were made by Sundays, Mondays, Tuesdays, Wednesdays and Thursdays. The restaurant managers should alter the entertainment programs for these days: the contribution to risk made by Fridays and Saturdays was insignificant.

169

Days,

Z2 0.18382 0.16912 0.16912 0.17647 0.02941 0.00735 0.26471

Months,

Z1 0.14706 0.14706 0.13235 0.15441 0.02941 0.02941 0.02206 0.00735 0.01471 0.00735 0.16176 0.14706

Gradations

1 2 3 4 5 6 7 8 9 10 11 12

Advertising Z3 0.375 0.625

Contributions of gradations Team, Staff qualification, Z4 Z5 0.47059 0.30882 0.15441 0.42664 0.22794 0.26471 0.14706 Z6 0.30882 0.29412 0.31618 0.05882 0.02206

Menu,

Type of evening, Z7 0.90441 0 0.00735 0.08823

Table 29. Probabilities of events-gradations in the risk of the restaurant’s failure with Yad=125.000 rubles (Nad=136; Risk=0.372603; N=365)

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Z3 – advertisement: the largest contributions to risk were made by advertisements in autumn and winter, hence they should be improved. Z4 – team type: the largest contribution to risk was made by the service team in autumn and winter, working on Mondays, Tuesdays, Wednesdays and Thursdays. Z5 – staff qualification: the largest contribution to risk was made by the staff; hence, the staff training period was not long enough. Z6 – type of menu: the largest contribution to risk was made by the first three menu types, and the least by the last two menu types. Z7 – event type: the largest contribution to the restaurant’s risk - usual, not festive occasions.

2.8.4. LP-analysis of Risk and the Efficiency of the Restaurant The transition was made from the LP-risk model of the “LPefficiency” class to the LP-risk model of the “LP-classification” class in accordance with the technique from section 1.7.4. The identification of the LP-risk model of the restaurant’s failure was performed on the basis of statistical data (Table 28). The identification technique development was performed using the admissible efficiency parameter value Yad = 125 thousand rubles; Nad = 136; Risk = 0.3726; N = 365. The following values were obtained: Fabs = 345 – the objective function value; Pmin = 0.1602 – the minimum state failure risk; Pmax= 0.5151 – the maximum state failure risk; dPc = 0.3549 – the interval of the state’s failure risk change; Pad = 0.3867 – admissible state failure risk; Pm = 0.3673 – the average restaurant’s state risk based on the LPmodel. In statistics there were Ng=229 good states and Nb=136 bad states. During identification there were Ngg=220 correctly recognized good states and Nbb=125 – bad states. The identification process by the gradients’ method converges approximately during 100 steps (Fig. 27). The peculiarity of the LP-risk model of the restaurant and its identification is factor Z2 “days of the week” and factors Z4 “team” and “event type” Z7, which depend on it, are repeated periodically. Therefore, there exist identical restaurant states. The group of repeated states has the same grades of parameters Z and can have different grades of the efficiency parameter Y.

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Fig. 27. The dynamics of the identification process

The transition from the LP-risk model of the LP-efficiency class to the LP-risk model of the LP-classification class is required for quantitative assessment and analysis of risk. The LP-efficiency model uses discrete historical data from the daily goods turnover of the restaurant. If we set the admissible value of the efficiency parameter Yad, then, using the restaurant performance statistics and condition Yi < Yad, we might calculate the number of the restaurant’s states Nad , which occurred in “the tail”. Let us call these states bad ones, and all the rest – good ones. The restaurant’s failure risk is determined by the equation (141) Risk=Pad=Nb / N . Let us find the frequency (probability) of occurring in “the tail” for the grade of each parameter: P2jr=Njr / Nad , j=1,2, …, n; r=1,2, …, Nj. The sum of probabilities P2jr for each parameter equals 1, because event-grades constitute the IEG. The probabilities P2jr determine the significance of events-grades for failure risk and for the efficiency of the restaurant’s performance. This significance might be used for taking decisions concerning the management of the restaurant. For example, the entertainment program of Monday events might be changed in order to attract more customers.

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Using LP-efficiency models we cannot determine the significance of parameters themselves for the risk of failure and efficiency of the restaurant. Therefore, the transition is made from LP-efficiency models to LP-classification models. Let us assign only two grades, 0 – the bad state, 1 – the good state, to the efficiency parameter (goods turnover) of the restaurant’s state Y as a random value depending on the condition Yi < Yad. Thus, let us substitute the actual values of goods turnover in thousands of rubles with only two grades 0 and 1. Then let us make a transition to the systems of LPequations (18 – 19). The condition Pi > Pad also divides the restaurant’s states into good and bad ones, but it is already divided by the state risk value. During the identification process we will calculate the risks of all states of the restaurant and build the distribution of the states risks. This will give us an opportunity to solve not only the task of assessing the significance of events-grades of parameters Z, but also the task of defining the significance of parameters Z1, Z2,…,Zn for the restaurant's failure and efficiency risk. To do this let us calculate the average risks Pjm of parameters in the “tail” of the states risks distribution. The significance of the parameters and grades obtained depends on the given admissible value of the efficiency parameter Pad. The following conclusions were made based on identification results: x Repeated groups of states do not hinder the process of identifying the LP risk model of the restaurant’s performance, x If in a group of states there are some states with different values of the efficiency parameter Y grades, it reduces the accuracy of the LP-risk model. LP-analysis of risk and efficiency. We have built the distribution of the restaurant’s goods turnover and made the transition from the LP-risk model of the “LP-efficiency” class (Fig. 4) to the LP-risk model of the “LP-classification” class (Fig. 3). During the identification of the P-risk model the probabilities of grades Pjr, P1jr, P2jr (Table 30) were calculated and the following conclusions were made: x The risk in different months differs nearly tenfold. x The first months of the restaurant’s operation are the most risky ones (11, 12, 1, 2, 3, 4).

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Table 30. Probabilities of events-gradations after identification

Pjr P1jr P2jr 1. Months, Z1 0.10899 0.14255 0.08493 0.10195 0.13335 0.07671 0.10228 0.13378 0.08493 0.10996 0.14382 0.08219 0.05683 0.07434 0.08493 0.02365 0.03094 0.08219 0.02703 0.03535 0.08493 0.00649 0.00849 0.08493 0.00657 0.00859 0.08219 0.00895 0.01171 0.08493 0.07844 0.10259 0.08219 0.13339 0.17446 0.08493 5. Staff 0.05723 0.27850 0.1671 0.07093 0.34517 0.24657 0.07733 0.37633 0.58630

Pjr P1jr P2jr 2. Days, Z2 0.05918 0.13371 0.14246 0.05124 0.11578 0.14246 0.06066 0.13705 0.14520 0.09711 0.21941 0.14246 0.01519 0.03433 0.14246 0.00411 0.00929 0.14246 0.15509 0.35042 0.14246

6. Type of menu 0.09781 0.30484 0.16712 0.07280 0.22690 0.16164 0.13010 0.40549 0.25205 0.01518 0.04732 0.25205 0.00495 0.01544 0.16712

Pjr P1jr P2jr 3. Advertising 0.05229 0.41245 0.50411 0.07449 0.58755 0.49589

4. Type of team 0.08987 0.37620 0.28493 0.05705 0.23883 0.21096 0.05416 0.22674 0.28767 0.03780 0.15822 0.21644

7. Type of evening 0.07914 0.89330 0.77808 0.00026 0.00293 0.09315 0.00061 0.00693 0.02192 0.00858 0.09684 0.10411

x The risk by days also varies nearly tenfold. Friday and Saturday are less risky (grades 5, 6). x The risk from both types of advertising (1, 2) is nearly the same. The risk depending on team type differs nearly twofold (1, 4).

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x The risk depending on the staff qualification (1, 2, 3) is nearly the same. x The risk depending on the menu type is 25 times bigger (3, 5). The menu of the fifth type is the least risky. x The risk depending on the event type varies nearly 400 times: 1 – a usual event has the highest risk, 2 – an event with a banquet has the lowest risk. The contributions of parameters to the accuracy of the LP-risk model (the objective function) were studied. The parameter “days” has the largest contribution. Its exclusion decreases the objective function by 51 units. The parameter “staff qualification” has the smallest contribution.

2.8.5. Risk Analysis by Contributions of Parameters The analysis of the restaurant’s risk and efficiency by contributions of parameters is conducted for “the tail” of the goods turnover distribution. The average values of probabilities for the whole distribution and only in “the tail” are shown in Table 31. Table 31. Analysis of significance of the parameters for failure risk of the restaurant (Yad=125.0)

Parameters

Pjm all

Pjmb – in “tail”

1

0.06242

0.09822

2

0.06209

0.08572

3

0.06236

0.06620

4

0.06249

0.08210

5

0.07103

0.06826

6

0.05986

0.09499

7

0.06444

0.07223

The efficiency parameter risk Y is proportionate to the probabilities of influencing parameters Z. Therefore the average values of probabilities Pjm of the grades of influencing parameters Z in the IEG could be treated as the significance of the parameters for the average efficiency parameter risk.

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Table 31 (column 2) gives the average values of probabilities of Pjm of the grades of the parameters in the IEG for all restaurant states (Y change range). Column 3 gives the average values of probabilities of Pjm of the grades of the parameters in the IEG for “the tail” of the distribution of the restaurant’s states efficiency parameter under the condition that Y < 125 thousand roubles, i. ɟ. for bad states. On the basis of the obtained results we can make the following conclusions. For the whole Y interval change the contributions of parameters to the average risk Pjm are nearly the same. x The significance of the average risk parameters changes depending on “the tail” value, The significance of parameters differs twofold. For “the tail” Y < 125 thousand rubles – parameter 1 (months) has the largest significance and parameter 3 (advertising) – the smallest. For “the tail” Y < 75 thousand rubles parameter 1 (months) has the largest significance and parameter 7 (type of event) – the smallest. x The difference between the significance of parameters in risk grows as the admissible value of the efficiency parameter decreases. The technology of the restaurant business risk and efficiency management could also be applied to other public catering facilities, as well as to mass service stores. The statistical DB is created on the basis of daily monitoring of the object’s operations.

2.9. LP-models of Failure of Management of ZAO “Transas” A manager-to-be must be able to set goals and realize them, take long term risks, calculate all risks, select the justified risk, take strategic decisions, perform several functions, view business as a whole. Peter Drucker

The management of the SES under study, belonging to the group of local SES-3 for companies and firms, depends basically on their wishes and possibilities. We discuss here the LP-risk model of management’s failure with regard to: functions, activity directions, achieving of the aim or a group of aims, performance management [65, 66]. The LP-risk models of management failure (of the company, the city hall, the government, the project, etc.) are important for management efficiency.

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2.9.1. State of the Problem As the great economist Peter Drucker noted [63], a manager-to-be must be able to set goals and realize them, take long term risks, calculate all risks, select the justified risk, take strategic decisions, perform several functions and view business as a whole. The literature analysis revealed that there are virtually no methods and models of business management on the basis of risk, that common sense cannot be transformed into a risk model, that there is no common approach to managing different risks in business. Lots of Russian and foreign authors describe the situations where management-related decisions are taken, for example in the textbook for universities and colleges [64]. Cases and precedents often bear the same names as problems, letters, seminar topics, etc. Some of these materials are presented by the presidents of famous companies. The most wellknown precedents are those of the major companies: General Motors, U.Steel, IBM, Digital Equipment, McDonnell Douglas, General Electric, Toyota Motor, Ford, Chrysler, etc. Special attention should be given to work [83], which represents an attempt to introduce intellectual methods in management. Using management situations only from one company it is impossible to build a management model or an expert system due to the scarcity of statistical data. Every element of the situation has several values, and the number of possible situations is a googol. Management lacks decision taking models. At the same time an LP-failure risk model can be built for management purposes.

2.9.2. Characteristics of the Company The ZAO “Transas” company (TRANsport SAfety Systems) is a producer of high-technology products popular all over the world. Unlike many other companies Transas sells the products which it itself has developed. The company has a noble mission - to reduce risk and the cost of management systems in sea and air transport [65, 66]. The ZAO “Transas” company offers a full range of pre-commissioning and maintenance activities with regard to supplied equipment. A network of service offices was created, and is being maintained and expanded for these purposes. Transas customers include shipping and fishery companies, owners of small vessels and yachts, the naval and military industrial sector, administration of ports and shore services, civilian

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aviation and military air forces, educational and training institutions, rescue services and oil-mining companies. The phenomenal success of the “Transas” company during the difficult transitional period of business development in Russia needs to be scientifically generalized and its management experience has to be systematized. The financial success of “Transas” company is largely based on strategic management experience of its world business.

2.9.3. Failure of Management by Functions Let us describe the scenario of the company’s management failure risk in accordance with its functions: staff management, strategic planning, marketing and sales, record keeping, etc. Let us denote the functions by Lvariables Z1, Z2,…,Zn. The structural model of failure risk management is presented in Figure 28. The scenario of management failure risk in accordance with functions is formulated as follows: the management failure happens due to failure with regard to one, two … or all functions. L- and P-risk models of management failure are written down as expressions like (13 – 17). If the probabilities of IE failure are higher than 0.05, failure risk (convergence to 1) happens if the number of IE and their probabilities increases.

Y

Z1

...

Zj

...

Zn

Fig. 28. Structural model of management failure risk

The saturation of probabilities (risk convergence to 1) happens when the number of IE and their probabilities grows. The L-risk model of the company’s failure to achieve its aims at the stage (Fig. 29) is as follows: (141) Y = Y1 ∨ Y2 ∨ ... ∨ Y j ∨ ... ∨ Yn , j = 1,2,..., n.

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Y

Yj

Y1 ...

Z11 . . . Z1N1

Yn .

Zj1 . . . ZjNj

Zn1 . . . ZnNn

Fig. 29. The structural model of failure risk of achieving groups of targets

Let us make a transition from the logical description of failure risk in achieving the aim to the arithmetic one. The P-model of failure risk in achieving the aim is: P = P1 + P2 (1 − P1 ) + P3 (1 − P1 )(1 − P2 ) + .... (142)

2.9.4. Failure of Management by Business Direction Let us deal with the company’s failure risk scenario with regard to directions of activities: shore systems, naval on-board equipment, integrated complexes, aeroplane on-board equipment, aeronautic support, maritime and flight simulators. Let us denote the directions of the company’s activities by L-variables Z1, Z2,…,Zn and the corresponding amount of finance by E1, E2,…, En. The structural risk model in accordance with the directions of activities is presented in Fig. 29 and the LP-risk model is defined by the equations of type (141 – 143). The possible losses of the company due to failure equal: P = P1 + P2 (1 − P1 ) + P3 (1 − P1 )(1 − P2 ) + .... (143) where P1,…., Pn are failure probabilities in accordance with the directions of activities. Let us calculate the company’s failure risk with regard to three P3, four P4 and five P5 directions of activities with L-addition of risks and arithmetic addition. The results of arithmetic addition and L-addition of risk events are quite different. During arithmetic addition we add up weights and might get an absurd result: the company’s failure risk is more

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than one. The example also demonstrates the need for the company’s disintegration when the number of the directions of its activities is growing, because the risk might become inadmissible.

2.9.5. Failure of Management in Achieving of Objectives Groups In 2000–2005 the strategic aims of ZAO “Transas” concerned business development [65]. The tasks of strengthening its position in the market were solved by creating the commercial image of the Russian Federation. Five groups of strategic objectives Y1,Y2,…,Y5, were defined. Each group included several subsidiary objectives (Fig. 29): Y1 – defense capacity consolidation: Z11 – implementation of new techniques in the market for military technology and dual goods; Z12 – improvement of tactical and technical characteristics of military equipment; Z13 – extension of high-tech products markets; Z14 – increase of military equipment operation safety; Y2 – the integration of the Russian Federation into the world economic environment: Z21 – the improvement of the business image of the Russian Federation; Z22 – the increase of the foreign capital investment potential; Z23 – foreign debt; Z24 – the development of the State debt market of the Russian Federation and the inclusion of ZAO “Transas” in foreign debt redemption programmes; Y3 – the creation of conditions allowing the Russian Federation to join The World Trade Organization: Z31 – the integration in the world economic environment; Z32 – strengthening of external economic ties; Z33 – the improvement of the North-West region’s transport infrastructure. Y4 – branding of St. Petersburg as the cultural and sci-tech capital of Russia: Z41 – attraction of investments to St. Petersburg; Z42 – the improvement of St. Petersburg’s historical center image; Z43 – development of information technologies and creation of technological clusters in St. Petersburg; Z44 – acquisition of capital assets for centralizing the management and production assets of ZAO “Transas”;

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Y5 – centralization of ZAO “Transas” management: Z51 – increase of the company’s management efficiency; Z52 – the restructuring of the company with the aim of further successful business development, including new directions. We have built the L- and the P-risk models of the company’s failure to achieve its strategic objectives. Vectors Y, Y1, …,Y4, Y5 and their components are random events, which are denoted as L-variables by the same identifiers. Let us formulate the scenario of the risk of failure to reach one group of objectives by the company in the following manner: the group of objectives will not be achieved, if one objective from the group is not achieved, or any two objectives or all the objectives from the group. The structural risk model of achieving a group of objectives Yi is presented in Fig. 37. If objectives Zi1, Zi2, …, Zin belong to Yi , then we have the following L-model of the risk of the failure to reach the objective: P P1  P2 (1  P1 )  P3 (1  P1 )(1  P2 )  .... (144) The L-function of the risk of failure to reach the objective after the orthogonalization of

Yi

Z i1 › Z i 2 › ... › Z in .

(145)

P-polynomial of the risk of failure to reach the objective

Pi

Pi1  Pi 2 (1  Pi1 )  Pi 3 (1  Pi1 )(1  Pi 2 )  ....

(146)

Example. Let us consider the failure risk in achiviing the first group of objectives Y1 : Yi = Zi1 OR Zi2 OR … OR Zin.

The L-function of the risk of failure to reach the objective after the orthogonalization of Yi = Zi1 OR Zi2 NOT Zi1 OR Zi3 NOT Zi2 NOT Zi3 OR …. Pi = Pi1 + Pi2 (1 – Pi1) + Pi3(1 – Pi1)(1 – Pi2) + …. Example. Let us analyze the risk of the failure to achieve the first objectives group Y1. The assessments of failure probabilities using NIIexpert information equal: P11=0.05; P12=0.04; P13=0.03; P14=0.06. Then the risk of failure to reach the group of objectives Y1 equals: P1 = 0.05+0.04·0.95+0.03 · 0.96 · 0.95 + 0.06 · 0.95 · 0.96 · 0.97 = 0.1684.

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The structural risk model of the failure to achieve several groups of objectives at the stage of the strategic development of the company is presented in Fig. 36. Let us consider the risk of failure in achieving all groups of objectives without writing out the expressions for achieving each of the objectives. The L-risk model of the failure in achieving all the company’s objectives at the stage (147) Y = Y1 OR Y2 OR ... OR Yj OR … OR Yn, j = 1, 2, … , n. The P-model (P-polynomial) of the risk of the failure to achieve the objective P = P1 + P2 (1 – P1) + P3 (1 – P1) (1 – P2) + …. Example. The risk of the failure to achieve objectives Y1 and Y2 is considered. The probability of failure in achieving a group of objectives Y1 was calculated earlier and it was equal to P1=0.1684; the probability of failure in achieving the objective Y2 equals P2=0.075. The risk of failure in achieving the group of objectives Y1 and Y2 equals P = 1– 0.8315 · 0.925=0.2308.

2.9.6. Management of Quality Functioning of the Company In many countries quality assessment systems are known as National Prizes, and they are used to stimulate the quality of products (services) and improve their marketability, and to encourage the companies to implement modern and effective quality management techniques. For example, in Russia there exists the RF Government Prize in the sphere of quality, which was founded in 1996. Quality centers deal with consultations and assessment of the documents supplied for the competition for the Prize. The information, provided by the company, is strictly confidential. A group of independent, highly professional experts, who have received special training, give their assessment of the company's quality management system. The quality management systems are self-assessed once a year. Fig. 30 provides the maximum numerical evaluation of criteria in points for the model of the RF Government Prize in the sphere of quality. The sum of all maximum points equals 1000. It is recommended to use the presented distribution of points by criteria for any enterprise and organization regardless of the branch of industry, size and property type.

100 points

Leadership

CAPABILITIES – 550 points

100 points

Resources

.

120 points

Business Results

RESULTS –450 points

– 60 points

Society Results

120 points

100 points

90 points

Customer Results

130 points

Processes

People Results

Policy Strategy

120 points

People management

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Fig. 30. The model of quality assessment in business (excellence in business)

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“The target group” of the company itself makes the self-assessment of the company’s quality system. It assesses each criterion Z1 – Z9 in points and calculates the ratio of this assessment to the maximum possible value. The system of participating in competitions allows an assessment of the achieved criteria level as percentages of the maximum possible values. At the same time we have an objective picture of the shortcomings of the company with regard to each criterion and direction of activity. The company’s achievements are determined by comparing the numerical values of criteria Z1 – Z9 for different years. The quality management of the whole of the company’s activities is analyzed, including finances, resources, staff, etc. The Russian standard of quality assessment and management is used (which is close to American, European and Japanese standards) [12, 13]. The quality model criteria have been divided into two categories: possibilities and results. The category “possibilities” Z10 is determined by assessing the following criteria: the role of management in the organization of production Z1, the use of employees’ potential Z2, planning and strategy in the sphere of quality Z3, use of resources Z4, technology of production, advertisement, service Z5. The category “results” Z11 is determined by assessing the criteria of the satisfaction of all persons concerned: executives Z6, consumers Z7, society Z8 and finances Z9. We have proposed to modernize the company’s performance quality model, i.e. to replace the arithmetical addition of events-factors (in points) with the logical addition of their probabilities (relative weights). Let us build the structural, logical and probabilistic risk models of quality and market losses. Let us denote the random events, corresponding to quality criteria, by the same logical variables Z1 – Z9, the “quality” property, by the logical variable Y and derivative events “Possibilities” and “Results” – Z10 and Z11, correspondingly. Let us build the structural risk model of quality losses (Fig. 31) or the failure model with logical connections OR.

Z1

Z2

Z10

Z3

Z4

Y

Z5

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Fig. 31. The structural risk model of company performance management

184

Z6

Z7

Z11

Z8

Z9

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The L-risk model of the company’s performance quality failure:

Z1 › Z 2 › ... › Z 8 › Z 9 .

Y1

(148)

The L-risk model of the company’s performance quality failure in orthogonal form:

Y

Z1 › Z 2 Z1 › Z 3 Z 2 Z1 › ... › The P-risk model of the company’s performance quality failure:

P (Y

1)

P1  P2Q1  P3Q1Q2 )  ....

(149)

The criteria of the company “Transas” performance quality grew by years, but the growth was different for different criteria. The L-criterion of quality is accurate and transparent. Here we should also employ the synthesis of the probabilities of events, based on NII-expert information, received from experts. Further on all received assessments are combined with account of the weights of the experts themselves. In conclusion, we would like to stress that a company (private or State) can use risk management technologies for assessing the probabilities of success in solving its difficult economic problems. The success probability depends on the wishes and possibilities of the subjects participating in the process: for example, the State AND (logic AND) a company, AND competitors, AND banks, AND scientists developers of risk management technologies, AND public opinion. It is impossible to solve difficult socioeconomic problems efficiently without scientists and public opinion. If the success of solving a problem depends only on the company itself (its capital, staff and management), then such a problem should not be considered complex and it is sufficient to use the above mentioned LP-risk models of the company’s management failure.

CHAPTER THREE SPECIAL SOFTWARE FOR PROBLEMS OF ECONOMIC SAFETY

The computer makes it possible to solve the problems which did not exist before its invention. IT news “data Æ the model explaining the data”

The software for managing the socioeconomic safety of SES is so important for the assessment, analysis, management and forecasting of risk that top-economics and LP-risk models of SES cannot exist without it. The construction of LP-risk models, their identification on the basis of statistical data, risk analysis, forecasting and management have a high computational complexity and can be performed only with the help of computers and special LP-Software. Let us describe the developed software, used now for LP-risk models of different classes, which has been tested in research with real data. It has been used in teaching situations for many years.

3.1. Software “Arbiter” for the Modeling of Structure-logic Software “Arbiter” [16, 69, 70] provides the following functions: x automated modeling and calculation of reliability parameters for structurally complex systems, including nuclear power stations and other hazardous industrial objects; x automated modeling and calculation of probabilities of emergency situations and accidents at hazardous industrial objects. Software “Arbiter” is based on a general logical and probabilistic method (GLPM) of system analysis and realizes the technology of automated structural logical modeling (ASLM) of complex systems. Software “Arbiter” was attested by Rostekhnadzor of the Russian Federation in 2007 and this is the first software in Russia which is based

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on GLPM realizing the new technology of monotonous and nonmonotonous logical and probabilistic analysis (modeling and calculation of parameters) of reliability and safety of structurally complex system objects of various designations. In “Arbiter” there are four modes for modeling and calculations: x static mode (the initial data are probabilistic parameters of elements); x in-time-probabilistic mode (the initial data are parameters of exponential distributions of mean time between failures); x approximate calculation mode (realizes typical calculation methods for fault trees); x logical and statistical mode.

Fig. 32. Basic windows of “Arbiter”

Software “Arbiter” gives an opportunity to perform correctly all widespread monotonous structural schemes (fault trees, block diagrams, connectivity graphs, etc.) and a new class of non-monotonous structural models of systems. Such possibilities are provided by the description of the studied properties of systems with the help of schemes of functional completeness (SFC) which use a full set of logic algebra operations: AND, OR and NOT. At present software “Arbiter” is used in 30 organizations, including 12 higher educational institutions. For educational centers the software

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“Arbiter” is supplied in network version with 15 workstations at a discount price. The developer provides an information service and consulting at the first stage of practical application of “Arbiter” in reliability analysis of structurally complex systems, and at the stage of solving complex tasks with the use of logical and probabilistic modeling in various fields of activity. For modeling and analysis of socioeconomic systems (SES) and information security analysis, the adopted version of software “Arbiter” was developed (“Arbiter-AT”) which is being tested now in educational and scientific organizations in Saint Petersburg. In comparison with the full version, this software makes it possible to perform logical and probabilistic modeling in the static mode only (Fig. 32). From the viewpoint of dimensions and accuracy of algorithms the adopted version is identical to the full version. Taking into account that the adopted version “Arbiter-AT” is designated for educational goals, the screen interface was changed by the substitution of the terms from reliability analysis with the terms of GLPM, and the option of exporting simulation results in Excel was improved.

3.2. Software “ROCS 2” for Analysis of Risk of Big Systems The techniques and the software complex are described in V.A. Prourzin’s works [68], where the reader can find the methods and algorithms of analysis and optimization of safety and risk of large systems, based on building failure trees. Special attention is paid to the methods of solving high dimensionality problems. The author has built effective algorithms for calculating probabilistic measures and damage from undesirable random events (failures, accidents, etc.) connected with the system performance. At the heart of it lies the well-known LP-approach [9], based on the representation of dangerous and undesirable events connected with system performance (failures, accidents, etc.) as random binary events, described by two states. In their turn these events depend on a certain number of primary binary random events (the failure of an element, the failure of the operating personnel to do certain actions, the presence of external effects, etc.). The problems arising here are mainly connected with dimensionality. All known methods, anyway, come down to building logical functions which allow us to calculate the probability of the main event based on probabilities of elementary events. These functions are, in fact, the

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polynomial from primary events. Already in the case when there are only several dozens of primary events, the number of elements can be very big. In this case the PC memory may not be enough for writing down such a polynomial. The work proposes methods of reducing memory capacity and the amount of calculations when working with large systems. Two basic approaches to the formalization of working capacity conditions and system safety are used. Working capacity can be presented 1) with the help of structural schemes and functional integrity schemes [9, 16] or 2) with the help of failure trees (of events) [69]. These approaches are universal and interchangeable. A certain approach is selected due to personal preferences and convenience of use. In the work these conditions are set by building the trees of events. The top of such a tree is formed by an undesirable event (failure, breakdown, catastrophe, etc.). Logical functions of conjunction, disjunction and negation are used to connect this event and elementary events. We differentiate between simple trees in which every elementary event appears only once and trees with repeated elements. The universal method of determining a system’s working capacity and safety within the framework of the LP-approach is the method based on defining the set of the shortest paths of performance. Such description is equivalent to setting a two-level tree. The method of coding linear (logical) form is used in order to reduce computer storage capacity. The operations with encoded variables are introduced. The encoded summary (conjunct) is more compact than a symbolic one. The obtained benefit is the speed of calculations. The main difficulty of working with large systems is the fact that the computer storage capacity required for logging the L-function might turn out to be extremely large even when the encoding method is used. We do not have to build the structural L-function for calculating the probabilities in the case of simple event trees containing no repeated elements. The calculation of events probabilities is performed with the help of the simple algorithm based on recursive functions. When we calculate probabilities in the case of event trees with repeated elements we use the modified LP-method [9], based on the mixed form of the probability function. The structural L-function is built only for the subset of elementary events appearing more than once in the tree. For other variables we insert the values of their probabilities at once. Thus, we obtain the structural function with fewer variables. The algorithm realizing this approach has a familiar structure, except for the fact that the operations are performed not with probabilities, but with sequences of codes. When the calculations are made in the tree for

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each L-variable we have to check whether all its appearances in the tree structure have been taken into account. If this condition is satisfied, we perform the operation of inserting the probability value for this variable, mentioning similar terms. As a result, the number of L-variables in the structural function decreases.

3.3. Software “Cortege Algebra” for Arbitrary Logic Functions The software based on cortege algebra (CȺ) is aimed at calculating the probabilities of arbitrary logical functions of logic algebra (propositional calculus), including the system with multi-state logical variables. Let us list the examples of applications where cortege algebra has been employed: x The logical analysis of verbal proofs with different variants of formulae of propositions and predicates calculus. The expert system model of car diagnostics was used as an example of the search for a conclusion. x The calculation of the probabilities of logical functions: the bridge scheme with two and three states, the solution of I. Ryabinin’s problem, etc. x The determination of students’ intellectual preferences (the paper in the journal “Modeling in applied science research”- XVI, 2008); x The solution of the “Antitrust problem” using deductive databases; x The development of an expert system, aimed at taking decisions at the level of the ship’s captain, in case of emergencies on board a ship or in other places, in particular in combat conditions; x Analysis of the processes of collecting, processing and evaluating data by the example of the information analytical system of the educational establishment, etc. Basic terms and structures of cortege algebra. Cortege algebra (CA) is based on Cartesian products of sets and is in fact a many-relationship relations algebra [71, 72]. CA research has shown that it can be used to present the following structures of discrete mathematics: tables; relation algebra structures; graphs, schemes and networks; predicates and mathematical logic formulae; discrete automatons; artificial intelligence systems (rules, frames, semantic networks, etc). This great variety of representations allows us to unify miscellaneous pieces of information in a general mathematical description. The

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theoretical foundation of CA contains a number of definitions and theorems which help to solve the following problems: x its isomorphism with the following systems is substantiated: the algebra of sets, the many-relationship relations theory and multisort predicate calculus; x the algorithmic basis for solving various problems of logical analysis of systems is being developed (logical derivation, correct hypotheses and “hidden axioms” search, etc.); x this system is immersed in probabilistic space. Many-relationship relations in CȺ can be represented by means of four types of structures (to be discussed further); these are called CA-objects. Each CA-object is immersed in a certain attributes space. The names of CA-objects contain an identifier to which we add the sequence of attributes names in square brackets. They determine the relation scheme in which this CA-object is set. For example, notation R [XYZ] means that the space of CA attributes-object R is X, Y, Z. CȺ is based on the properties of the Cartesian product of sets and on the general mathematical definition of ɚ polyadic relation. If we have the attributes space X, Y,…, Z, then the relation in this space is a certain definite subset of the Cartesian product of the domains of attributes: X, Y, …, Z. CA-objects are a contracted mapping of many-relationship. If necessary, with the help of certain algorithms they could be transformed into usual many-relationship consisting of the sets of cortege elements (in CA these corteges are called elementary corteges). CA-objects of the same type are the structures set in the same attributes space. In CȺ we can perform all set-theoretical operations not only with same type of relations, but also with the relations with different schemes. CAobjects (C-corteges, C-system, D-corteges, D-system) are formed as matrixes. Their cells contain not the elements, but the subsets of attributes domains. These subsets are called components. They include two fictitious components: the full component (denoted by an asterisk) is a set equal to the domain of the corresponding (according to its position in the cortege) attribute and the empty set –*. ɋ-systems are convenient instruments for representing disjunctive normal forms of finite predicates. Let us call the ɋ-system consisting of one line – the ɋ-cortege (analogous to the row vector in matrix algebra). A separate conjunct corresponds to the ɋ-cortege in logic.

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With the help of D-systems in CȺ we can model conjunctive normal forms of finite predicates. The D-system is denoted by the matrix of components-sets, limited by inverse square brackets. Logical probabilistic analysis in cortege algebra. The logical probabilistic analysis (LPȺ) of the systems represented by L-functions was developed by I. Ryabinin and his scientific school. These methods use basically propositional calculus formulae as mathematical models, analyzed with regard to the reliability and safety of structurally complex systems - it means that only systems with two states are studied. Multistate systems (i.ɟ. with more than two states) in LPȺ are represented only by individual cases. Research has shown that cortege algebra is one of the potential mathematical tools of LP-analysis with wider modeling opportunities. It allows LP-modeling of multi-state systems. Conclusion. The research results above demonstrate the fact that cortege algebra is a mathematical system which allows us to unify various data structures in intellectual systems and use the algebraic approach in the logical analysis of information and control systems. The structures of cortege algebra agree well with the architecture of modern computers and possess natural parallelism, which allows a comparatively easy realization of intellectual systems in concurrent processing of computer complexes. CȺ makes it possible to solve the direct and inverse problems of Panalysis of L-systems in multidimensional space.

3.4. Software for the Class “LP-classification” This software was developed for identifying LP-risk models using statistical data, for the purposes of assessment and analysis of the credit risks of natural persons and legal entities, and it is also used for the assessment and analysis of bribery risk as well as in other classification problems [12, 56, 57]. The LP-models for the assessment and analysis of credit risks, as well as special logical software, were created and studied during 10 years. They were tested using the data from one Western bank (1000 loans) and two Russian banks. The following tasks have been solved: 1. Construction of the crediting risk model using the statistics of the bank, calculation of the risk attributes of the set of loans and analysis of the bank’s crediting activities. 2. Calculation of risk and loan attributes, loan risk analysis. The software builds the LP-risk model using the statistical data of the bank. The LP-risk model is identified by solving the optimization

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problem by the random search or the gradient method using statistical data. The non-commercial version of the software is used for teaching and demonstration purposes. We will only mention its functions without describing the screen forms: x a package of 1000 loans of physical persons: 700 – good ones and 300 – bad ones; x a loan is described by 20 parameters; x a parameter has gradations, there are 96 of them in total. The demo-version recognizes correctly 822 loans out of 1000, unlike 750 loans in the known scoring techniques and models on the basis of neural networks. The problems to be solved: 1. Loan risk assessment consists in determining risk attributes in the LP-credit risk model, trained on the basis of statistics. 2. Loan risk analysis – the determination of the contributions of the grades. When the loan risk is calculated the probabilities of initiating events are added logically in accordance with the Lmodel. The grade contribution to the risk in the loan is proportionate to its probability. 3. Identification of the LP-credit risk model. The screen form provides the parameters for the optimization formula by the Monte-Carlo method: the number of optimization steps Nopt, the number of Monte-Carlo modeling attempts at the optimization step Nmc, average risk by statistical data Pav, the design number of good loans for the LP-model Ngc, the coefficient in the optimization formula K1. These parameters are set before training, but can be altered by the user. The screen form also provides the current values of parameters in the dynamics of training LP-risk models: the achieved maximum value of the objective function Fabs, the achieved maximum value of the objective function at the optimization step Fmax (due to the operation of leaving deadlocks, Fabs and Fmax may not coincide), the number of incorrectly recognized bad loans Nbg, the number of Monte-Carlo attempts at the optimization step Nmc, the current value of admissible risk Pad, the difference between the maximum and the minimum loan risks Pc, the number of the current optimization Nv. The training process is started by the button “Run training”, and ended by the “Exit” button. The initial values of probabilities P1jr, j=1, 2,…,n; r =1, 2,…,Nj can be found in the file Original-P1.txt. The optimal values

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of the probabilities of events-grades (there are 96 of them in this problem) are written down in the file Proby-P1.txt and the file Proby-P.txt. The integral parameters of training LP-risk models are presented in the file fMaxLast-risk.txt for the last optimal step of the LP-model identification. 4. Analysis of the bank’s crediting activities. The contributions of parameters to the objective function are calculated by pushing the button “Analysis” on the screen form. Simultaneously the parameters are excluded automatically one by one and the model is retrained. The number of optimizations for retraining is set to be less than during the initial training of the LP-risk model, say, Nopt=50. The research results in the file FMaxA.txt make it possible to define the most relevant parameters. For the bank under study the parameters with a zero contribution could be excluded from the description of loans. 5. The contributions of parameters to average risk are determined for the whole set of loans. The probabilities of grades for this parameter are added and the sum is divided by the total number of loans. The research results are in the file FMaxLast.txt. Special attention should be paid to parameters making the biggest contribution to average risk. The probabilities of events-grades and their contributions to the accuracy of the model for all 20 parameters can be found in the file FMmaxLast.txt.

3.5. Software for the Class “LP-efficiency” This software complex is designed for the selection, assessment and risk analysis of the investment portfolio [12, 13, 73]. Let us name only the software functions without describing the screen forms: 1) the automatized input of companies’ stock quotations into the DB of the system using Internet open resources; 2) the creation of prices and yields graphs using the shares of specific companies or market indexes. The time period and observation intervals are specified; 3) the construction of the portfolio by selecting the necessary shares and specifying the initial shares of invested capital; 4) the support of several portfolios simultaneously; 5) the automatic revaluation of the portfolio cost on the basis of the latest prices; 6) the display of money distribution diagrams according to assets;

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7) the calculation of statistics parameters on the basis of portfolio assets; 8) the modeling of the yield discrete distribution for the specified time horizon by several techniques: accounting for dependencies between assets, without accounting for dependencies and accounting for dependency on the factor; 9) the diagram representation of the portfolio yield distribution; the following portfolio parameters are displayed on the screen: average yield, standard deviation, minimal admissible yield for specified risk, the risk for assigned yield; 10) the verification of yield distribution modeling by historical data; 11) portfolio structure optimization based on one of the criteria: the maximization of admissible yield for the assigned risk, risk minimization with assigned yield; 12) the calculation of portfolio management efficiency characteristics (Sharp’s coefficients, portfolio dispersion, etc.) and their comparison with the market sample and with each other; 13) the calculation of the contributions of the shares grades to risk and portfolio yield.

3.6. Software for the Synthesis of Events Probabilities Software for the synthesis of events probabilities is essential for LPrisk models of the new type. We mean here LP-risk models with expert assessment of events probabilities: hybrid LP-models, conceptual LPmodels and LP-models for managing the OpR of a bank. For these models we have built techniques of the synthesis of IE probabilities for LP-risk models based on the aggregate randomized indexes technique using expert NII-information. The newly created software complex Expa with its convenient service for the synthesis and analysis of events probabilities has been described. Risk management technologies in structurally complex systems (RMT SCS) with LP-risk models have been used successfully for solving various applied problems. This project is very important, because the sustainable and safe development of the country requires effective management of SES on the basis of the newly introduced type of LP-risk models and events. In this new type of LP-risk models the tasks of the synthesis of events probabilities on the basis of expert NII-information have emerged. For hybrid and conceptual LP-risk models a special software complex was developed with a convenient service for the synthesis of events probabilities.

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New types of events and LP-risk models. Events-propositions have been introduced: 1. Signal events for the correction of IE of LP-risk models: x in economy (fluctuations of currency exchange rate, tax rate changes, etc.); x in politics (the President’s speeches, joining the EU, etc.); x in legislation; x in innovations (emergence of new service types, etc.); x in natural disasters and wars. 2. Events of the successful solution of the problem by: x the State; x business; x banks; x scientists; x public opinion. 3. Conceptual events-propositions. 4. Indicative events. New types of LP-risk models have been introduced: x Hybrid LP-models according to risk scenarios for the subjects taking part in the solution of the problem and, for objects-tasks, constituting the core of the problem. x Conceptual LP-models, in which the system risk scenario is written on the basis of the descriptions by specialists who understand the nature of the problem. x The P-model of invalidity. x Indicative LP-risk models. The synthesis of initiating events probabilities for LP-risk models. The system development modeling is equivalent to making forecasts in conditions of uncertainty. Consequently, in LP-technologies of managing the risk of SES condition and development, when there is no other data, the probabilities of events are assessed on the basis of expert NIIinformation. The synthesis of IE probabilities is performed on the basis of the aggregate indexes method by NII-information [14, 74]. An expert cannot make an exact assessment of the probability of one event. His assessment will be more accurate and objective if he considers 2 to 4 alternative hypotheses (an expert is “rocked”). The software for the synthesis and analysis of events probabilities. At the first stages of research in hybrid and conceptual LP-risk models the

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software complex ASPID-3W, developed by N.V. Hovanov and his team, was used [74]. The main purpose of this complex is the classification and ranking of economic and technical objects. ASPID-3W can essentially solve the tasks of the synthesis of events probabilities, but in order to obtain the necessary results we have to omit or perform formally nearly half of the operations (there are nearly forty of them) of the software complex manual. This causes some difficulties, even when students do their laboratory work. Therefore, a task was set to create a simple-to-use software complex with a convenient service for the synthesis of events probabilities. There are plenty of mathematical methods of expert data processing. The method of randomized aggregate indexes [7, 74] is the most suitable one. It allows aggregating the opinions of several experts into a single index. The key feature and advantage of the method is its use of expert NII-information. Let us explain the term “NII-information”. “Nonnumerical” means ordinal information. The expert could restrict himself to the assertion that the probability of one event is higher than the probability of the other event, i.e. with the inequality. “Inaccurate” means interval. The expert could say that the event probability lies in the interval from 0,2 to 0,5. “Incomplete” means that, strictly speaking, this information is not sufficient to find the definite target values. An extra advantage of the above approach is the possibility of expert and statistical data synthesis. In such a case the statistics can be regarded as an extra expert’s opinion. The method of randomized aggregate indexes presents certain computational difficulties due to the fact that a lot of variants have to be searched. For that reason the Expa software should be used [75]. It allows solving the task of synthesis and analysis of events probabilities and automatizing the decision-making process in conditions of uncertainty. Fig. 33 presents the external type of the software complex in the variables definition mode. The term “variable” is used for generality. In this case probabilities are understood as variables. The working algorithm looks as follows: x In section 1 (window) the list of variables is typed. x In the same section admissible intervals (interval information) are assigned. x In section 2 relations are introduced (ordinal information). x Modeling accuracy (0,01; 0,02; 0,04; 0,05) is assigned in the control bar and the number of possible alternate solutions (316251) is calculated automatically. x The calculations are started; the results are displayed in section 1. The report can also be presented in Word format.

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If the aggregate assessments of many experts have to be determined, the alternatives selection mode is used (Fig. 34): x The list of experts is introduced in section 4; x The admissible intervals for the weights of each expert are assigned (columns); x The values of assessments from each expert are assigned in section 5. x Preference relation for experts is introduced in section 6. x Modeling accuracy is assigned (0,01; 0,02; 0,04; 0,05); x The calculations are started; the results are displayed on the screen (Fig.35).

Fig. 33. Program Expa (the synthesis of alternative probabilities) 1 – section of variables; 2 – section of relations; 3 – section of calculations results

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Fig. 34. Program Expa (obtaining of aggregate assessments from several experts) 4 – the list of experts; 5 – the table with the values of assessments from each expert; 6 – the correlation table for the weights of experts

Fig. 35. Program Expa (calculations results for several experts): 7 – calculated weights of experts; 8 – aggregate assessments of probabilities

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3.7. The Scheme of Modeling and Analysis of Risk in the Big System It is quite easy to logically combine SES LP-risk models without common repeated events. In this case we must act as usual: each SES must be modeled and studied separately, then the risks should be joined by Lconnections OR, AND. We will get the aggregate result for a big system. However, when we try to logically combine LP-risk models of many different socioeconomic systems (for instance n=10), each having about 20 initiating events and repeated initiating events, the following course of action should be taken: 1. Develop the structural, logical and probabilistic risk models for every SES from groups: SE-1, SE-2, SE-3. Using these models for each system, determine their risks, significance and contributions of IE in the corresponding system. 2. Find repeated events R1, R2,…,Rm. in LP-models LP1, LP2, …,LPn of corresponding systems. 3. Represent the LP-model of each SES from repeated events included in it and the remaining IE. Build the L-risk model for remaining IEs, perform their orthogonalization, build the corresponding Ppolynomials and calculate risk. 4. In the end we will obtain the L-risk function for all SES without repeated events: Y1, Y2,…,Yn, orthogonal L-risk functions Yort1, …,Yortn, corresponding P-polynomials and probabilities P1, P2,…,Pn. 5. Let us denote the obtained L-functions Yort1, …,Yortn by L-variables Z1, Z2,…,Zn. 6. On the basis of the structural scheme of the combination of different socioeconomic systems build one large SES from repeated events R1, R2, …,Rm and L-variables of derivative events Z1, Z2,…, Zn. Naturally, each repeated event for all SES is denoted by the same L-variables. 7. Using the usual rules and orthogonalization, perform quantitative modeling and quantitative risk analysis of the large SES, assigning numerical values to the probabilities of repeated events R1, R2,…,Rm and the values of probabilities P1, P2,…, Pn of L-functions of derivative events Z1, Z2,…,Zn, calculated earlier. 8. Calculate the risk of the large combined E, significance and contributions of repeated events R1, R2,…,Rm and derivative events Z1, Z2,…,Zn.

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3.8 What Maths is needed for Economics? Special software for top-economics has been developed, realizing the technology of management of socioeconomic safety based on logical and probabilistic (LP) risk models. There are definitions of invalidity in economics and top-economics, new kinds of Boolean events-propositions and new kinds of LP-risk models (hybrid, conceptual, invalid, indicative) on the basis of events-propositions. But, to make a transition from LP-calculus and logical models to probabilistic models and their application, we need new special mathematical techniques and algorithms which are absent from classic mathematics. They are designed for management of socioeconomic safety, research and laboratory works. Special mathematical methods for the technology of management of socioeconomic safety and the bases of LPcalculus have to be studied by students and specialists. Top-economics and software use the following new mathematics [8, 13, 14, 56, 68, 71, 73]: 1. The concept of invalidity in the economy, by analogy with reliability in engineering. 2. New Boolean events-propositions in economics: the event of objects’ failure (government, business, banks, academics, public opinion); signaling events (in economics, politics, legislation, innovation, natural disasters and changes in the global market); events of invalidity of systems, processes and products; conceptual developments, statements predicting risk; events-propositions indicative of danger states; events-propositions about the latent character of surveys and data from social networks; incompatible events. 3. Logical and probabilistic calculus (LP-calculus) for eventspropositions. 4. New LP-risk models with events-propositions: hybrid LP-risk models of the failure to solve difficult social and economic problems; the invalid LP-risk model of systems, processes and products; conceptual LP-models forecasting systems and processes; indicative LP-models of system danger. 5. The method of summarizing randomized indicators to assess the probabilities of events. 6. The methods of building LP-risk models of SES. 7. Techniques of LP-analysis of SES risk. 8. Methods of LP-management of SES risk.

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9. Special software Expa and Arbiter for calculations and laboratory work in the training course “Top-economics”. 10. The method of identification for non-linear tasks with many real valued variables (about a hundred) and integer optimization criteria (the number of recognized objects). 11. Inability to generate the equivalent training and testing samples in the problems of objects classification (credit) given to indicators of gradations. 12. The algorithm of the exception of incorrect and old data in the problems of classification of objects (credits). 13. The management algorithm of banks and enterprises on contributions of random events to the “tails” of the distribution of the efficiency parameter. 14. The replacement algorithm of the LP-risk model in the classification problems after the formation and analysis of signaling parties of objects. 15. The algorithm of transition from the efficiency LP-model to the LP-risk model of prediction in the state space. 16. Bayes’ formula with a limited amount of information. 17. The algorithm converting any tabular database into a tabular knowledge base.

3.9. Sets of Software for Different Classes of LP-risk Models Below you will find the summary table of software for the classes “LP-modeling”, “LP-classification”, “LP-efficiency”, “LP-forecasting” and “Hybrid LP-risk models”. These classes use various software (Table 32). Table 32. Software for the classes of LP-risk models

N 1

Name of class LP-modeling

2 3

LP-classification LP-efficiency

4

LP-forecasting

Set of Software Software Arbiter, Expa, ROCS 2, Cortege Algebra Software for management of credit risks Software for management of efficiency of enterprise and portfolio risk Software for credit risks management, Software for management of portfolio risk and enterprise efficiency

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Software Arbiter, Expa, ROCS 2, Cortege Algebra, Software for credit risks management, Software for portfolio risk management and enterprise efficiency

The software for the “LP-efficiency” class has a software module which calculates the frequency and probabilistic contributions of eventsgrades of initiating parameters to the tail of the efficiency parameter distribution during a predetermined number of the last system states. The graphs of these contributions’ variance allow forecasting the crisis of the economic system. In an engineering system these graphs are compared for the new system (for instance, the gas-compressor unit of a compressor station of the main gas pipeline) and the system currently in service. Thus, the system exhaustion is assessed and the possibility of its future operation is predicted. The classes of LP-risk models use different software types. The “LP-forecasting” class and “Hybrid LP-models” are the most dependent on numerous pieces of software. Manual structural logic simulation. Some scientists and researchers solve the problem of structural and logic simulation “by hand”. They build risk scenarios, write the L-risk function, and perform its conversion into an orthogonal form on paper, using the method of conditional probabilities. They program the resulting B-polynomial in the Excel table, perform design studies and publish scorecards. Professor N. V. Hovanov conducts laboratory works at the department of “Economic Cybernetics” in this way.

CHAPTER FOUR STATE OF THE PROBLEM OF MANAGEMENT OF ECONOMIC SAFETY

Technological innovations and innovations in management, especially in State management, must be treated on an equal basis. Li Keqiang

The work on the creation of LP-risk models of SES began about 10 years ago when the LP-credit risk management model was developed [56– 59]. It was followed by development and research into about a dozen different LP-risk models in the economy, described in [12, 13]. Now we are going to substantiate the importance and fundamental character of the problems related to the management of SES economic safety. Academic disciplines Micro- and Macroeconomics do not deal with the problems and tasks of socioeconomic safety management. Therefore, a new discipline “top-economics” with its own methods, models, technologies, tasks and SES had to be developed. The main task of this discipline is socioeconomic safety management.

4.1. Relevance of the Problem of Management of Economic Safety The safety of any country depends not only on military, technical, technological, energy and information safety, but, to an even greater extent, on economic safety, i.e. on the sustainable development of SES, counteraction to corruption, bribery and drug addiction, the management of the system of innovations, etc. Socioeconomic safety management and SES management do not belong to top priority fundamental directions in science, defined by the Government of the Russian Federation and RAS. The Russian Scientific Foundation also offers no grants for research in economic safety management.

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At present economic safety management is guided by its own rules, which are very different and changeable, depending on the subjects setting them. We propose to make a transition to the management, guided by universal rules of risk management technologies in structurally complex systems, with logical probabilistic risk models. The Nobel Prize winners James Buchanan and James Heckman [2, 3], academicians A. G. Aganbegyan, V. L. Makarov, R. S. Grinberg and A. I. Tatarkin [4, 5, 6] in their works deal with the connections between economy and politics in the development of the State and its socioeconomic safety maintenance on the basis of the theory of games, modeling and statistical data analysis. The present book introduces a new academic discipline “topeconomics”. It is done for the purposes of analysis, forecasting and management of economic safety and SES of the country. The novelty of “top-economics” consists in the introduction of invalidity by analogy with reliability in engineering, new types of Boolean events-propositions, new types of LP-models, new techniques and tasks for risk management in different SES of the country and its regions. The main branches of economics (micro- and macroeconomics) do not tackle the problems of economic safety management of the country. A high degree of problems specification in these disciplines prevents us from building mathematical models of economic safety management, SES condition and the system of innovations of the country. LP-risk models of SES economic safety do not require much sophistication. There are three groups of SES in top-economics: SES-1 which are of top priority for the country; they are aimed at reducing financial losses and increasing the revenues; SES-2 are complex ones for the country and the regions, depending on several ministries; SES-3 are local ones, for companies and firms. We propose a concept of economic safety management of the country, which combines the management of socioeconomic systems. Resources are required for managing the State and development of SES. Therefore, we also include into SES the innovations’ management system, aimed at reducing losses and increasing revenues from industry and business. We have adopted the principle of the Chinese leader Li Keqiang according to which technological innovations are viewed as equal to innovations in management, including State management. The possibilities of the management of the economy of the country and its regions can be significantly extended and improved if, alongside microand macroeconomics, we use “top-economics”.

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4.2. Fundamentals of the Problem of Socioeconomic Safety Management This work is the first one to have established the scientific foundations of the logical probabilistic management of the socioeconomic safety risk of the country and its SES [12, 13]. The tasks of the new academic discipline “top economics” include assessment, analysis, forecasting and management of economic safety of the country and its SES. We have proposed new types of Boolean events-propositions, new types of LP-risk models and SES risk management technologies. We have proposed hybrid LP-models for assessing the risk of failure in solving difficult socioeconomic problems. We have proposed invalidity LP-models for the assessment of systems and quality of products by WTO, conceptual LPrisk models of system development failure, indicative LP-risk models of system state danger, LP-models of the banks’ operational risks and capital reservation by Basel. We have created and tested risk management technologies in structurally complex systems. They include the following components: LP-calculus, classes of LP-risk models, procedures of assessment, analysis, risk forecasting and management; the technique of events probabilities synthesis in LP-risk models based on expert NII-information, special software for classes and procedures, examples of applications and the training course. The work describes formal, associative, tabular and other methods of building LP-risk models for the purposes of economic safety management. It introduces the techniques of LP-risk analysis, LP-forecasting of risk in the space of States and the LP-management of complex SES state and development risk. It also describes the techniques of accounting for LPrisk models’ responsiveness and the synthesis of events probabilities in LP-risk models based on expert NII-information. Risk in economy is also tackled in some works based on classical methods of probability theory and mathematical statistics [74, 75, 83 – 86]. A review of literature on the application of LP-risk models can be found in I. Ⱥ. Ryabinin’s work [10]. Although the above works do not deal with the problem of SES economic safety management, they are certainly of great interest to economists. Also, there exist the following fundamental problems of socioeconomic safety management:. x Application of various types of databases for LP-management of risk and efficiency of systems;

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x Construction of hybrid LP-risk models for management of socioeconomic systems, problems and countries; x Management of national safety of countries.

4.3. Realization of the Problem of Economic Safety Management Top-economics for SES economic safety management was realized and tested on the basis of example applications (see chapter 2) and publications. In group SES-1, containing the SES of top priority for the State and aimed at reducing losses and increasing revenues, the following SES were developed and studied: 1. The management of the system of innovations. 2. Counteraction to bribery and corruption. 3. Counteraction to drug addiction. 4. The management of the banks’ operating risk and capital reservation by Basel. 5. Systems and products quality management by WTO. 6. The monitoring and management of crediting process in banks. Research results were published in Russian and foreign journals. In group SES-2, containing complex SES for the State and the regions, the following SES were developed and studied together with the students of economics from SUAI: 1) The LP-model of the failure to solve housing construction problems, 2) The LP-risk model of birth rate state, 3) The LP-risk model of death rate state, 4) The LP-risk model of inflation growth, 5) The LP-risk model of economic growth retardation, 6) The LP-risk model of depression in agriculture, 7) The LP-risk model of small and medium enterprise development failure, 8) The LP-risk model of an environmental disaster, 9) The LP-risk model of real wages decrease, 10) The LP-risk model of unemployment growth, 11) The LP-risk model of the educational system failure, 12) The LP-risk model of the healthcare system failure,

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13) The LP-risk model of the failure to solve the problem of lack of kindergartens, 14) The LP-model of the failure to solve cultural problems, 15) The LP-model of the failure to solve the IT development problem. We have developed the LP-model of the current situation with economic safety in Russia. Research results on topics 1), 2) and 15) were published in Russian and foreign journals. In group SES-3, containing local SES for companies, the successful management of which basically depends on the wishes and possibilities of companies themselves, the following SES were developed and studied: 1) LP-management of the risk and efficiency of the restaurant “Prestige”, 2) LP-assessment of ratings and comparison of office centers in St. Petersburg, 3) The LP-risk model of the failure of ZAO “Balt-Avto-Poisk”, 4) The LP-risk models of ZAO “Transas” management’s failure, 5) The LP-risk model of a construction company, 6) The LP-risk model of an explosion in an ammunition depot, 7) The LP-model of the reliability of electrical supply in an iron and steel works, 8) The LP-model of the insurance against explosions and fires at hazardous facilities. Research results were published in articles and books [12, 13]. We have created and tested risk management technologies in structurally complex systems. They include the following components: LP-calculus, classes of LP-risk models, procedures of assessment, analysis, risk forecasting and management; the technique of events probabilities synthesis in LP-risk models based on expert NII-information, special software for classes and procedures, applications examples and a training course. We have created and tested special software for solving economic safety problems: ACM for structural and logical modeling, LP-software for forecasting system risk in the states space, LP-software for managing the risk of the investment portfolio and the earning power of enterprises; Expa – for the synthesis of events probabilities using NII-expert information. The following facts were revealed on the basis of the analysis of topeconomics applications with real data:

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x Complex socioeconomic problems cannot be solved without scientists and public opinion. x The creation of effective SES and the system of innovations management is impossible without reforms in education, science and economy. x In order to achieve the widespread use of LP-risk models we have to develop special inexpensive software and retrain specialists, managers and university teachers of economics. The development of top-economics has lasted nearly 10 years. Techniques, LP-risk models, technologies and problems for different applications in assessment, analysis, forecasting and management of economic safety were created. The results obtained were published in seven books in Russian and English [7, 8, 18, 33, 76, 77, 78], five PhD dissertations in Economics and Technology (V. V. Karasev, V. V. Alexeev, Yu. N. Lebedev, E. V. Alexandrova, E. I. Karasevɚ), more than 30 peer-reviewed articles in Russian and foreign journals (The Journal of Economic Theory, Management Problems, Risk Analysis Problems, Automatization and Telecommunications, IJ RAM etc.), two special editions of journals (International Journal of Risk Assessment and Management and Risk Analysis Problems) [79, 80], the Proceedings of twelve International Science Schools “Modeling and Analysis of Safety and Risk in Complex Systems” (SPb, IPME RAS, 2001–2016) [81], more than 200 laboratory and graduation works on LP-modeling and risk management in the Economics faculty of SUAI. The topics of the laboratory works of fifth-year economics students in SUAI, devoted to logical probabilistic risk models and selected by the students themselves, also present a certain interest: 1. Risk of the failure of economic revitalization in the Russian Federation. 2. Risk of a company’s development failure. 3. Risk of euro exchange rate fall. 4. Risk of the service system failure. 5. Risk of the President’s activity failure. 6. Risk of the President’s election failure. 7. Risk of a decrease in an enterprise’s profits. 8. Risk of world crisis. 9. Risk of political instability in the country. 10. Risk of civil unrest in the Russian Federation. 11. Risk of crisis in the Russian Federation. 12. Risk of failure of a company’s marketing strategy.

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13. Risk of decrease in oil prices. 14. Risk of the failure to solve a difficult economic problem. 15. Risk of bribery and corruption in a government body. 16. Risk of civil servants’ fraud. 17. Bribery risk in service. 18. The LP-risk model of getting a diploma. 19. The LP-risk model of a plane crash. 20. The LP-risk model of a forest fire. 21. The LP-risk model of non-fulfillment of the plan by a retail outlet. 22. The LP-risk model of increasing prices for a product.

4.4. Perspectives of Management Problem of Economic Safety There are new perspective problems in economic safety management. We have formulated and solved the important problem of database use (DB) for logical and probabilistic risk management and systems efficiency. The solution consists in converting a tabular database into a tabular knowledge base, writing down the system of logical equations and the LP-risk model, and analysis and management of the system’s risk. This allows us to expand significantly the management of risk and efficiency in the economy. We have presented a methodology of how to transform any tabular database (DB) into a tabular knowledge base (KB), based on the introduction of events-graduations for the system’s state variables, events of appearance of the system’s state and events of failure of the system’s state, and groups of incompatible events. We have given specific examples of the construction and use of LP-risk models for the following databases: a bank’s credit risk, a bank’s portfolio risk, and the risk and effectiveness of a restaurant. We have also described the special software for LPmanagement of risk and efficiency on the basis of database systems. Top-economics can be used in the management of the national safety of the country. It allows us to solve the following tasks: 1. Management of economic war with sanctions based on LP-risk models for socioeconomic systems; 2. Construction of LP-risk models of failure for following significant SES in national security: 3. Anti-corruption; 4. Combating drug addiction; 5. Management of innovation system in a country;

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6. Construction of hybrid LP-models for risk assessment and analysis of failures of complex systems, processes and national safety projects in a country. Development of top-economics is virtually impossible without the creation of a special software, “Arbiter: top-economics”. The problem of risk management in the economy is complex and necessitates a variety of tasks. The risk management techniques have five classes of LP-risk models: LP-modeling, LP-classification, LP-efficiency, LP-forecasting and hybrid LP-risk model. Each class has the following procedures: construction and orthogonalization of risk L-model; identification of LPmodel on statistical data; LP-analysis of risk and efficiency; LPmanagement of risk and efficiency; LP-forecasting risk and crisis; synthesis of event probabilities of LP-risk model by expert NII information. The construction, assessment, analysis, forecasting and risk management with the help of LP-models has a high computational complexity, therefore the perspectives of development and implementation of SES economic safety management problems depend on the availability of corresponding special software. There are no such software tools in economics. The commercial software complexes Arbiter and Relex [16, 67, 69], used for assessing the reliability of engineering systems are quite popular in technology. The software complex Arbiter was developed in St. Petersburg by A. S. Mozhaev and his team. The certification of this complex was preceded by numerous researches in the field of automatization of structural logical modeling and testing in many engineering applications. The use of the software complex Arbiter for the purposes of construction and analysis of LP-risk models in economics implies some difficulties for the following reasons: x The tasks of modeling and risk analysis are described in engineering and military terms which are quite unusual for economics: “reliability”, “safety”, “durability”, “robustness”, “the general LP-method”, “the functional integrity scheme”, etc.; x The complex contains some functions which are not necessary for risk assessment and analysis of risk in economics (fail-free operation, reconstruct ability, etc.); x The software complex contains no utilities for solving the problems which are quite widespread in economic safety: the synthesis of events probabilities using expert NII-information, the solution of

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identification (optimization) problems for forecasting system risk in the states space, etc. A special inexpensive software complex, which is currently codenamed “Arbiter: top-economics”, could be used for these purposes. Not all fundamental indexes describing the system state are used for SES economic safety management, but only indicative indexes, characterizing the system state danger. The number of such indexes is much smaller. There are usually about 20-30 IE in LP-risk models of SES, and the conjuncts in the logical risk model are not cumbersome. Economic safety management can be studied by separate SES, or by their logical combinations in twos, threes, etc. The development of the commercial complex “Arbiter: top-economics” has already begun. The following should be done: x The exclusion of technical and military terms in descriptions and instructions. x The exclusion of functions which are not necessary for socioeconomic safety modeling, analysis and management. x The creation of the database of texts of all examples of LP-models applications for SES economic safety management described in the present book. x Defining of events-propositions in short form for each SES. This is necessary, as some events-propositions can be repeated (occur) in different SES, and it is necessary to register all recurrent events. x The creation of the database of scenarios of IE action for the purposes of synthesising their probabilities using expert NIIinformation. x The inclusion of utilities in the complex for solving the tasks of synthesising IE probabilities using expert information and solving identification problems by statistical data for forecasting system risk in the space of state, etc.

4.5. The need for Reform of Education, Science and Economy The drawbacks in management of the innovations’ system and in management of the economic safety of some SES, mentioned below, prove the fact that there is an urgent need for reforms in education, science and economy in the country. The following drawbacks were revealed in the educational system:

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x The learning programs and competence lists for training economy students in accordance with the Bologna process do not correspond to the economic situation in Russia. x Western closed techniques and non-transparent software are not efficient for training students, or for assessing the credit risks and ratings of banks and companies. The Russian Academy of Sciences does not: x support the emergence and development of innovations in the country. x select fundamental and priority research directions in economics objectively. x allocate funds for research fairly and objectively due to the existence of clans within the Academy. x encourage the solution of complex problems at the intersection of disciplines. The Government does not: x encourage the participation of scientists and public opinion in the solution of difficult socioeconomic problems. x support economic safety management of the country. x select top priority research directions objectively. x encourage contacts between Russian and Western scientists. x employ the social justice principle in its work. x promote the creation of an innovations’ management system.

4.6. The need to Improve Construction Strategies for the Socioeconomic Evolution of Regions The need for reforms is also substantiated by the analysis of the methods and techniques of developing the strategy for the economic and social development of St. Petersburg till 2030 [82]. Similar strategies have also been developed for the other regions of the country. The strategy for the economic and social development of St. Petersburg includes the current economic indexes and future indexes till 2030. The following shortcomings have been revealed in the strategy of economic and social development: 1. It contains no mathematical models for managing the risk of SES state and development.

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2. It uses the Western SWOT-analysis technique, which appeared in the early 1960s. A long time has passed since then. New ideas, techniques, models and software have appeared. 3. It lacks any assessment of the risk of SES and the condition of processes. It makes no mention of the following problems: counteraction to bribery and corruption, counteraction to the growth of drug abuse in the country, management of the innovations’ system, the assessment of OpR of the banks and capital reservation by Basel, the management of performance and products quality by WTO, the management of economic wars with sanctions, etc. 4. The risk of solving difficult socioeconomic problems is not assessed. These problems are solved by the government, business, banks, public opinion and scientists. The fact that difficult socioeconomic problems cannot be solved without public opinion and scientists is ignored. It is not specified how we should take into account signal events in economy, politics, law, innovations, natural disasters and wars to change socioeconomic indexes and make amendments to the strategy. 5. LP-risk models and special LP-Software are not used. SES states are described by lots of indexes. Non-linear optimization problems are solved by very cumbersome calculations. It is impossible to forecast a SES state without special software for risk assessment, analysis, forecasting and management. 6. According to the strategy, the successful economic development of the country does not presuppose reforms in education, science and economy. 7. The strategy has to be updated constantly on the basis of events in economy, politics, law, innovations, natural disasters and wars. Socioeconomic indexes of the country change constantly. The strategies approved by the Government, the State Duma and regional authorities are bound just to lie uselessly till 2030. A strategy must be built up as a dynamic system; it must be constantly elaborated, amended and documented depending on signal events in the economy, politics, law, the world market, innovations, natural disasters and wars, as well as the decisions and declarations of the country’s leaders. The Federal government, local governments and the Russian foundation of research in priority science directions might finance the creation of techniques, models, technologies and the programmes of dynamic development strategies of the country and its regions.

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4.7. Subject Index of the Discipline “Socioeconomic Safety Management” These are the following indirect symptoms of stagnation in economic science: 1. Publishing houses are not requiring expertise inputs for publications because publications, in general, have no innovative ideas. 2. It is not clear what mathematics is required to teach economists. This fact is obvious from the programme of the First International Scientific and Methodological Conference “Mathematical Education of Economics Students”, Saint-Petersburg, March 25, 2016, Saint-Petersburg State Economic University. 3. Publishing houses specializing in economics do not accept materials prepared in LATex editor but require the Microsoft Word format with a limited set of tools and without style files. 4. Textbooks and monographs have no subject indexes. Let us consider some questions in detail. Text editors. Publishing houses, which specialize in economics, ask the authors to present books and papers for publication prepared in the Microsoft Word format. Economic publications are mostly unvaried and contain “works of art” about economics with illustrations of time series of various indicators, which, in the authors’ opinions, allow the making of decisions. Publishing houses, which specialize in mathematics, mechanics and other exact sciences, require materials for publications to be prepared in LATex. Publications in the LATex editor have various tools, style files and possibilities for automated formatting of references, indexes, formula numbers, tables, figures and their sizes. Every section is placed on a new right page, and it is convenient to read and sell the electronic version of the section which is interesting for a client. In spite of the existing rules, the author prefers LATex. It offers great advantages for describing LP models and compiling subject indexes. Subject indexes. Subject indexes are absent from books devoted to economics. This fact only proves that there are few new concepts and results, as well as a kind of misunderstanding concerning the importance of indexes for the structure of knowledge about a research subject. Foreign publishing agencies do not accept books without a list of indexes. However, the subject index of this monograph is quite long and extensive. It includes three directions of research: components of top-

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economics, top-economics features, top-economics condition. In general, it has 26 sections, including 143 subject indexes. The sections of the subject indexes with the number of indexes in brackets are provided below: 1. Risk analysis in socioeconomic systems (6 indexes); 2. Boolean events-propositions in economic management (8); 3. Dynamics of LP-risk models (5); 4. Advantages and features of top-economics (12); 5. Classes of LP-risk models (5); 6. Components of top-economics (7); 7. Top-economics models (4); 8. Monitoring and crediting process control in banks (4); 9. Invalidity (4); 10. Objects of top-economics (3); 11. Operational risk in banks and capital reservation under Basel requirements (3); 12. Examples of SES applications in top-economics (10); 13. Counteraction to bribes and corruptions (4); 14. Counteraction to narcotization (3); 15. Procedures of technology for classes (6); 16. SES-1 are most important for country (6); 17. Features of top-economics (12); 18. Synthesis of probabilities of events for LP risk models (3); 19. Specialized software (10); 20. Condition of top-economics (6); 21. Risk management technologies (4); 22. Top-economics (3); 23. Quality management by WTO (2); 24. Risk management in SES (4); 25. Risk management in the innovations’ system of the country (4); 26. Management of risk of economic state of Russia (5). Thus, the contents and the subject index give the main idea of this monograph and help the reader to acquire and structure new knowledge.

CONCLUSION

Top-economics has unified a system of models, and has offered methods, technologies, and software for the management of economic safety of SES with varying complexity. We propose the name “topeconomics” for a unified system of knowledge and methods based on LPmodels and LP-calculus. Top-economics has its own methods, models, technologies, objects, tasks and special software. It considers the problem of safety management which is not addressed by macroeconomics or microeconomics. Nobel laureates George Buchanan and George Heckman investigated the relationship of economy and politics in the development of the State on the basis of game theory and analysis of statistical data. Expanding their ideas, the author proposes a new approach to the analysis and management of economic safety based on top-economics. Top-economics considers the relationship of economics, politics, business, science and society in a broad aspect. It takes into account initiating events which depend on the decisions made by the Government and on laws passed, and deals with the probabilities the State, business, scientists and society have to solve the problems of SES. Top-economics also addresses the signal events of changes in the economy, in politics and in law, as well as innovations and the situation in the world market; it is used for the correction of probabilities of initiating events in the LP-risk model of SES. We have obtained and used the following new mathematical results in our software: new Boolean propositions-events in economics; new LP-risk models using propositions-events; LP-calculus with events-propositions; the method of non-linear optimization (identification) for problems with many real valued variables (about a hundred) and integer optimization criteria – the number of recognized objects; the method of randomized indicators summary to assess the probabilities of events; Cortege Algebra for risk assessment in systems with complex logic functions and many (multi-state) conditions; the method of presenting logical variables in binary codes and actions with them in risk models of large dimension; proof of the impossibility of forming the equivalent training and testing samples in the problems of classification of objects, defined parameters with gradations; the exception algorithm of incorrect and outdated data in the problems of objects classification; the algorithm of management of

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banks and enterprises in the contribution of random events to the “tails” of the distribution of the efficiency parameter; the replacement algorithm of LP-risk models in the problem of classification after the formation and analysis of signaling parties of objects; the algorithm of transition from the efficiency LP-model to the LP-model of risk prediction in the state space. We have formulated these new important problems for top-economics: x database use for risk management; x construction of hybrid LP-models for management of socioeconomic safety of systems, processes and countries; x national safety management. The development of top-economics is virtually impossible without the creation of the special software “Arbiter: top- economics”. The problem of risk management in top-economics is complex and has a variety of tasks. Risk management techniques have five classes of LP-risk models: LPmodeling, LP-classification, LP-efficiency, LP-forecasting and the hybrid LP-risk model. Each class has the following procedures: construction and orthogonalization of the L-risk model; the identification of the LP-model by statistical data; LP-analysis of risk and efficiency; LP-management of risk and efficiency; LP-forecasting of risk and crisis; synthesis of events probabilities of the LP-risk model by expert NII information. We should not limit ourselves to any single software tool but should develop a set of software and utilities. The most advanced software is “Arbiter”. It has State certification and allows the connection of other types of software as utilities. The general scheme of the economic safety management of a country, region and system (enterprise) by top-economics has five successive stages: 1. For comprehensive assessment of the economic safety of the system, we build the following LP-risk model: the hybrid risk model of the system failure; the conceptual model of forecasting the state of the system; the indicative LP-risk model of system state danger; the LP-model of system state invalidity. 2. We build (organize) the monitoring system: 1) the indicators of the system’s state; 2) signaling events of the environment; 3) innovation in the domestic and foreign markets. 3. We correct events-probabilities and construct risk models using monitoring results. 4. We evaluate and analyze the risk (invalidity) of a system’s state by the invalidity LP-model.

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5. We invest the available resources to reduce the system’s invalidity and to implement innovations in production and management. In recent years a number of works have been published that consider the risk of the economics based on the classical methods of probability theory, mathematical statistics and decision-making [83–88]. A review of publications on the use of LP-risk models has been done by I. A.Ryabinin [10]. Although these publications do not consider the problem of economic safety management of SES, they are interesting to economists and for the development of top- economics. Of particular interest is the book by the mathematician V. P. Odinets [88], who was the first to point out the role of LP-risk models for management decisions. Economic management can be improved if, in addition to the tasks of microeconomics and macroeconomics, the problems of economic safety management can be solved. Top-economics has a huge potential for managing the socioeconomic safety of countries like Russia, China, India, etc., which have similar problems in their economies.

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SUBJECT INDEX

Advantage and features of top-economics: analysis of SES by different models, 5, 33, 129 analysis, forecasting and risk management of system, 5, 172 association of LP-risk models in one model, 66 complexity of safety problem, 5 building LP-model of invalidity using one state of system, 92 connection of different SES through repeated events, 5, 66 connection of economics, government, scientists and society, 5, 129 dynamism of LP-models, 5, 49 interdisciplinary of topeconomics, 128 management of economic safety by risk criterion, 5 multi-state of system invalidity, 5 risk management, 141, 177 transparency of analysis and risk management, 171 Analysis of risk in socioeconomic systems: contributions in left and right tails of distributions, 33, 30 contributions of events to the plus and to the minus, 44, 66 dangerous events and their combinations, 70 economic wars with sanctions, 67

frequency analysis of events, 44, 171 structure and probabilistic signification of events, 44, 66 Anti-bribery and corruption: axiom of bribery and corruption, 95 LP-model of bribes risk in servicing, 105 LP-model of bribes risk in the institution, 98 LP-model of bribes risk of officials, 100 Anti-drug addiction country: conceptual LP-risk model of drug addiction, 112 hybrid LP-risk model of failure to combat drug abuse, 109 LP-model of the drug situation dangers, 121 Boolean events-propositions: conceptual events, 6, 121 events of objects’ failure, 11 events of subjects’ failure, 6, 112 incompatible events, 6, 26 indicative events, 6, 92 invalidity of events, 6, 66 latent events, 6, 112 repeated events, 66, 135 signal events, 6, 143 Classes of LP-risk models: hybrid LP-risk model, 11, 30 LP-classification, 30, 141 LP-efficiency, 30 LP-forecasting, 30 LP-modeling, 177

228

Subject Index

Components of top-economics: examples, 17, 30 methods of LP-calculus, 3, 29 new LP-models, 10, 14, 17 objects of management, 3, 128 special software, 29, 187, 196 tasks, 3, 30 management technologies, 29 Dynamism of LP-risk models: changing probabilities on monitoring data, 49, 143 changing the situation in the market, 49, 66 conduct reforms, 49, 214 emergence of signal events, 49, 92 increasing qualification, 49,171 Examples of LP-models of SES in top-economics: anti-bribery and corruption, 94 anti-drug policy of the country, 128 management of risk and efficiency of the restaurant, 171 management of system quality and products at the WTO, 141 monitoring and management of crediting banks, 145 operational risk and reservation of capital by Basel, 129 risk management of innovation system of the country, 92 risk management of Russia, 66 risk models of management of company, 176 Invalidity: definition of invalidity, 3 new Boolean eventspropositions in invalidity, 6 new LP-models of invalidity, 10 subjective and objective in invalidity, 53

Models of top-economics: conceptual LP-models of forecasting, 17, 128 hybrid LP-risk models of failure, 11 indicative LP-models of state danger of SES, 17 invalid LP-risk model, 14, 66 Monitoring and management of crediting: identification of LP-model of credit risk, 147, 151 impossibility of testing samples, 152 LP-model of credit risk, 146 managing the process of crediting, 154, 158 New problems in top-economics: database use for risk management, 207 construction of hybrid LPmodels for risk management, 207 management of national safety, 211 Objects in top-economics: SES-1 of the highest priority for the state, 1, 70, 94, 141 complex SES-2 for state and regions, 1, 66 local SES-3 for business and companies, 1, 176 Operational risk of bank and reservation of capital by Basel: integration of LP-risk models, 135 LP-model of capital reservation, 134 LP-models of the bank’s operational risk, 131 Procedures of technologies for classes: building risk models, 33, 37, 43 identification of LP-risk model, 33, 171 LP-analysis of risk, 33; 44

The Management of Socioeconomic Safety LP-forecasting risk, 33, 46 LP-management of risk, 33, 48 synthesis of probabilities of events, 50 Quality management of systems by WTO: construction of invalidity LPmodel, 141 description of invalidity events, 143 Risk management in SES: management of development risk, 48 management of economic wars, 67 regulation and management in economics, 52 risk management of state, 48 Risk management of the economic situation in Russia: the Nobels’ social justice concept, 59 LP-analysis of risk of economic state, 66 LP-management of economic war with sanctions, 67 LP-model of risk of economic state, 59 LP- risk management of economic evolution, 68 LP- risk management of economic state, 67 Risk management of the system of innovations: analysis of the design of innovations, 82 global innovation index of the country, 71 hybrid LP-model of the innovation system failure, 89 indicative LP-model of the innovations’ system danger, 92

229

SES-1 of the highest importance for the country: combating bribery and corruption, 94 combating drug addiction, 128 management and reservation of capital by Basel, 129 management of the country’s innovation system, 92 management of crediting risk, 143 quality management of systems and products by WTO, 141 Special software: algebra of corteges for any logic functions, 191 Arbiter for structural logic modeling, 187 circuit of modeling risk of large systems, 201 class of LP-classification, 193 class of LP-efficiency, 195 Expa for the synthesis of probabilities of events, 196 mathematics for economists, 202 Rocs 2 for analysis of the risk of large systems, 189 software-sets for classes of LPrisk models, 196 text editor and object indexes 216 State of top-economics: basis of problems, 207 improving strategies of evolution of countries, 214 level of the developing topeconomics, 208 prospects of top-economics, 211 the need of reform in education, science and economics, 213 urgency of the problem, 205

230

Subject Index

Synthesis of probabilities of events for LP-risk models: method of randomized indicators summary, 50 non-numeric, incomplete and inaccurate expert information, 50 synthesis of probabilities of initiating events, 51 Technologies of risk management: classes of risk models, 30 direction of research, 35 procedure of classes, 33 training course, 187, 196 The properties of top-economics: advantages and benefits, 3 Li Keqiang’s concept of innovation, 49 by the Nobels’ concept of management, 59

concept of management by signal events, 53 concepts and principles of management, 56 database and knowledge base, 21 definitions of invalidity, 3 dynamism of LP-risk models, 49 regulation and management, 52 subjective and objective in invalidity, 53 transparency of methods and models, 3 unforgotten knowledge, 54 Top-economics: components of top-economics, 1 properties of top-economics, 3, 5 state of top economics, 208