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

Bruce A. Larson

Agricultural Economics, 1992, vol. 7, issue 2, 91-107

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.

Date: 1992
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