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Maximum Principle for Stochastic Optimal Control Problem with Distributed Delays

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Abstract

This paper is concerned with a Pontryagin’s maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, we establish a necessary maximum principle and a sufficient verification theorem. In particular, we deal with the controlled stochastic system where the distributed delays enter both the state and the control. To explain the theoretical results, we apply them to a dynamic advertising problem.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Qixia Zhang

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  1. Qixia Zhang
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Correspondence to Qixia Zhang.

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The author is supported by the National Natural Science Foundation of China (11701214) and Shandong Provincial Natural Science Foundation, China (ZR2019MA045).

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Zhang, Q. Maximum Principle for Stochastic Optimal Control Problem with Distributed Delays. Acta Math Sci 41, 437–449 (2021). https://doi.org/10.1007/s10473-021-0208-z

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  • DOI: https://doi.org/10.1007/s10473-021-0208-z

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