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Principles of stochastic dynamic optimization in resource management: the continuous‐time case
Author(s) -
Larson Bruce A.
Publication year - 1992
Publication title -
agricultural economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.29
H-Index - 82
eISSN - 1574-0862
pISSN - 0169-5150
DOI - 10.1111/j.1574-0862.1992.tb00207.x
Subject(s) - lemma (botany) , stochastic control , stochastic differential equation , dynamic programming , mathematical optimization , optimal control , duality (order theory) , bellman equation , continuous time stochastic process , maximum principle , mathematics , stochastic modelling , hamilton–jacobi–bellman equation , state variable , control variable , stochastic process , mathematical economics , ecology , statistics , physics , poaceae , discrete mathematics , biology , thermodynamics
A wide range of problems in economics, agriculture, and natural resource management have been analyzed using continuous‐time optimal control models, where the state variables change over time in a stochastic manner. Using a firm‐level investment model and a model of environmental degradation, this paper provides a concise introduction to continuous‐time stochastic control techniques. The process used to derive the differential of a stochastic process is stressed and, in turn, is used to explain Ito's lemma, Bellman's equation, the Hamilton‐Jacobi equation, the maximum principle, and the expected dynamics of choice variables. A basic extension of the dynamic duality literature is also provided, where the Hamilton‐Jacobi equation is used to derive a stochastic and dynamic analogue of Hotelling's lemma.