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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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    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Duffie, Darrell & Geoffard, Pierre-Yves & Skiadas, Costis, 1994. "Efficient and equilibrium allocations with stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 133-146, March.
    4. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    5. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    6. Wang, Jing & Ru, Tingting & Xia, Jianwei & Wei, Yunliang & Wang, Zhen, 2019. "Finite-time synchronization for complex dynamic networks with semi-Markov switching topologies: An H∞ event-triggered control scheme," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 235-251.
    7. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    8. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
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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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