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

This is the authors' abstract. We don't add key points for this paper.

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.