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

Li Ma, Fangfang Sun and Xinfang Han ()
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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

Mathematics, 2024, vol. 12, issue 7, 1-19

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.

Keywords: optimal control; reflected McKean–Vlasov SDE; lifted function; backward stochastic partial differential equation; Neumann problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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