730 98 605KB
Spanish Pages [33] Year 2013
Table of contents :
Cover
Title page
Copyright page
Contenido
Introducción
Capítulo 1 Cálculo de variaciones
1.1. Condiciones de transversalidad
Capítulo 2 Control óptimo
2.1. Condiciones de transversalidad
2.2. Control óptimo con valor descontado
2.3. Horizonte infinito
Bibliografía
Documento N.° 87
Elementos de optimización dinámica Daniel Ricardo Casas Hernández
Facultad de Ciencias Económicas y Sociales Programa de Economía
Facultad de Ciencias Económicas y Sociales Programa de Economía Bogotá, D. C. 2013
ISSN: 1900-6187 © 2013 Oficina de Publicaciones Cra. 5 N.° 59A-44 Teléfono: 3 48 80 00 exts.: 1224-1227 Fax: 2 17 08 85 [email protected] Dirección editorial Guillermo Alberto González Triana Coordinación editorial Marcela Garzón Gualteros Corrección de estilo Pablo Emilio Daza Velásquez Diagramación Édgar Andrade Carátula Andrea Julieth Castellanos Leal Impresión Xpress Estudio Gráfico y Digital Mayo del 2013
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N (t) K(t) G = e−rt [P F (K, N ) − wN − Pk (K˙ + δK)]. N (t) K(t) d ! G = 0; dt K˙ D G!N − G!N˙ = 0; dt
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! e−rt [P FK − PK δ − PK r] = 0;
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T
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x(T ) = xT .
H = e−δt F (t, u, x) + λg(t, u, x).
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x(t0 ) = x0 .
U ∗ (t), X ∗ (t) λ∗ (t) U ∗ (t) X ∗ (t) t→∞
λ(t)[x(t) − x∗ (t)] ≥ 0.
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H = e−δt
t→∞
S(t) = 0.
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C + µ(rs − c), ˆ c! = 0; H 1 = µ. c
ˆ ! = − µ˙ = µr; H s
µ(t) = µ0 e−δt .
λ(t) = µ0 e−(r + δ)t , S = rs − c. 1 rt e , µ0 1 S − rs = − ert , µ0 tert S(t) = − + αert . µ0 C(t) =
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µ0 e(−r + δ)t [S(t) − S ∗ (t)] ≥ 0.
t→∞ S(t) = 0
t→∞
µ0 e
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&
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