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Martingale conditions for the optimal control of continuous time stochastic systems

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  • Striebel, Charlotte

Abstract

A martingale condition is shown to be sufficient for optimality in a generally formulated continuous time control problem. Under the additional assumption that the class of admissible control laws has an [epsilon]-lattice property, the same martingale property is shown also to be necessary for optimality. The method makes use of the P-ess inf of a class of measurable functions used by Rishel [4] in a less general formulation. The general result of the paper is applied to more specific Markov and stochastic differential equation models to obtain conditions for optimality for these models.

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  • Striebel, Charlotte, 1984. "Martingale conditions for the optimal control of continuous time stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 329-347, November.
    • Handle: RePEc:eee:spapps:v:18:y:1984:i:2:p:329-347
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    Cited by:

    1. Weijie Zhong, 2022. "Optimal Dynamic Information Acquisition," Econometrica, Econometric Society, vol. 90(4), pages 1537-1582, July.
    2. Borkar, V. S., 2003. "Dynamic programming for ergodic control with partial observations," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 293-310, February.

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