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Maximum Principle for Optimal Control of Mean-Field Backward Doubly SDEs with Delay

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  • Meng Wang

    (Shandong University)

Abstract

In this paper, we study the control problems of mean-field backward doubly stochastic differential equations with delay in the form of an integral with respect to a finite regular measure. Using the standard variational method, we introduce a new type of anticipated mean-field doubly stochastic differential equations as adjoint equations and derive a necessary condition in form of the maximum principle for optimal control. Under appropriate assumptions, the sufficiency of the maximum principle is also established. Our results can be applied to a certain class of linear quadratic control problems and be used to study the mean-field game for a pension fund model with delayed surplus.

Suggested Citation

  • Meng Wang, 2025. "Maximum Principle for Optimal Control of Mean-Field Backward Doubly SDEs with Delay," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-24, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02624-5
    DOI: 10.1007/s10957-025-02624-5
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    References listed on IDEAS

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    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    2. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    3. Li Chen & Jianhui Huang, 2015. "Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1112-1135, December.
    4. Guatteri, Giuseppina & Masiero, Federica & Orrieri, Carlo, 2017. "Stochastic maximum principle for SPDEs with delay," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2396-2427.
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