Principles of stochastic dynamic optimization in resource management: the continuous‐time case
用企业投资和环境退化两个模型，简明介绍连续时间随机控制技术，推导伊藤引理、贝尔曼方程等核心工具，并扩展动态对偶性，适合想了解随机动态优化方法的经济和资源管理研究者。
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.