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Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control

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  • Zhang, Huanjun
  • Yan, Zhiguo

Abstract

This paper investigates an optimal control problem driven by backward stochastic differential equation (BSDE) with two controllers – one is called deterministic controller and the other one is called random controller. Necessary and sufficient conditions for the mixed optimal control problem are derived. A linear-quadratic (LQ) case of the mixed optimal control problem is also studied. The mixed optimal controllers are explicitly expressed by the solution of a fully coupled mean-field forward–backward stochastic differential equation (SDE). One of novel features is that a kind of mean-field BSDE naturally arises from the research on the mixed optimal control problem. Finally, a product management problem is used to illustrate the theoretical results.

Suggested Citation

  • Zhang, Huanjun & Yan, Zhiguo, 2020. "Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308343
    DOI: 10.1016/j.amc.2019.124842
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    References listed on IDEAS

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    Cited by:

    1. Wang, Yu & Yan, Zhiguo, 2023. "Pareto-based Stackelberg differential game for stochastic systems with multi-followers," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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