Optimal control of a class of fully coupled forward-backward stochastic partial differential equations

Abstract

This paper investigates the optimal control problem for a class of fully coupled forward-backward stochastic partial differential equations (FBSPDEs). Based on the existence of a unique solution to such equations, we formulated the associated optimal control problem within a convex control domain. By employing the convex variational method, we derive the associated stochastic maximum principle (SMP) for the optimal control problem intrinsic to this system. Finally, to demonstrate the applicability of our theoretical results, we apply SMP to a class of linear quadratic problems and obtain explicit expressions for the unique optimal control.

Keywords

Forward-backward stochastic partial differential equation / Monotonicity condition / Stochastic maximum principle / Convex domain / Linear quadratic problem

Acknowledgements

Qingxin Meng was supported by the Key Projects of Natural Science Foundation of Zhejiang Province (Grant No. LZ22A010005) and the National Natural Science Foundation of China (Grant Nos. 12271158 and 11871121).

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