1973/05/01 by Mark H. Davis, Pravin Varaiya · 3 citations
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications
paper · doi:10.1137/0311020
openalex publication_date 1973/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
In this paper necessary and sufficient conditions for optimality are derived for systems described by stochastic differential equations with control based on partial observations. The solution of the system is defined in a way which permits a very wide class of admissible controls, and then Hamilton–Jacobi criteria for optimality are derived from a version of Bellman’s “principle of optimality.” The method of solution is based on a result of Girsanov : Wiener measure is transformed for each admissible control to the measure appropriate to a solution of the system equation. The optimality criteria are derived for three kinds of information pattern : partial observations (control based on the past of only certain components of the state), complete observations, and “Markov” observations (observation of the current state). Markov controls are shown to be minimizing in the class of those based on complete observations for system models of a suitable type. Finally, similar methods are applied to two-person zero-sum stochastic differential games and a version of Isaacs’ equation is derived.