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Controlled Reflected McKean–Vlasov SDEs and Neumann Problem for Backward SPDEs

Author

Listed:
  • Li Ma

    (Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

  • Fangfang Sun

    (Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

  • Xinfang Han

    (Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

Abstract

This paper is concerned with the stochastic optimal control problem of a 1-dimensional McKean–Vlasov stochastic differential equation (SDE) with reflection, of which the drift coefficient and diffusion coefficient can be both dependent on the state of the solution process along with its law and control. One backward stochastic partial differential equation (BSPDE) with the Neumann boundary condition can represent the value function of this control problem. Existence and uniqueness of the solution to the above equation are obtained. Finally, the optimal feedback control can be constructed by the BSPDE.

Suggested Citation

  • Li Ma & Fangfang Sun & Xinfang Han, 2024. "Controlled Reflected McKean–Vlasov SDEs and Neumann Problem for Backward SPDEs," Mathematics, MDPI, vol. 12(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1050-:d:1367915
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    References listed on IDEAS

    as
    1. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    2. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2727-2751.
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