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Stochastic Maximum Principle for Generalized Mean-Field Delay Control Problem

Author

Listed:
  • Hancheng Guo

    (University of Macau)

  • Jie Xiong

    (Southern University of Science and Technology)

  • Jiayu Zheng

    (Shenzhen MSU-BIT University)

Abstract

In this paper, we first derive the existence and uniqueness theorems for solutions to a class of generalized mean-field delay stochastic differential equations and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-field delay control problem. Since the state equation is distribution-depending, we define the adjoint equation as a MFABSDE in which all the derivatives of the coefficients are in Lions’ sense. We also provide a sufficient condition for the optimality of the control.

Suggested Citation

  • Hancheng Guo & Jie Xiong & Jiayu Zheng, 2024. "Stochastic Maximum Principle for Generalized Mean-Field Delay Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 352-377, April.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:1:d:10.1007_s10957-024-02398-2
    DOI: 10.1007/s10957-024-02398-2
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    References listed on IDEAS

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