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Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays

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Abstract

This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays. Not only the state variable, but also control variables of players involve discrete and distributed delays. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, the author establishes a necessary maximum principle and a sufficient verification theorem. To explain theoretical results, the author applies them to a dynamic advertising game 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.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11701214 and Shandong Provincial Natural Science Foundation, China under Grant No. ZR2019MA045.

This paper was recommended for publication by Editor YOU Keyou.

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Zhang, Q. Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays. J Syst Sci Complex 34, 572–587 (2021). https://doi.org/10.1007/s11424-020-9068-1

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  • DOI: https://doi.org/10.1007/s11424-020-9068-1

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