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Principles of stochastic dynamic optimization in resource management: the continuous‐time case

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  • Bruce A. Larson

Abstract

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.

Suggested Citation

  • Bruce A. Larson, 1992. "Principles of stochastic dynamic optimization in resource management: the continuous‐time case," Agricultural Economics, International Association of Agricultural Economists, vol. 7(2), pages 91-107, July.
    • Handle: RePEc:bla:agecon:v:7:y:1992:i:2:p:91-107
    DOI: 10.1111/j.1574-0862.1992.tb00207.x
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