Maximum Principle for Optimal Control of Fully Coupled Mean‐Field Forward‐Backward Stochastic Differential Equations With Teugels Martingales Under Partial Observation

ABSTRACT The necessary conditions for the optimal control of partially observed, fully coupled forward‐backward mean‐field stochastic differential equations driven by Teugels martingales are discussed in this paper. In this context, we make the assumption that the forward diffusion coefficient and the martingale coefficient are independent of the control variable, and the control domain may not necessarily be convex. For this class of optimal control problems, we derive the stochastic maximum principle based on the classical method of spike variations and the filtering techniques. The adjoint processes that are related to the variational equations are determined by the solutions of proposed forward‐backward stochastic differential equations in finite‐dimensional spaces. Further, the Hamiltonian function is used to obtain the maximum principle for the optimality of the given control system. Our results are then applied to the mean‐field type problem of linear quadratic stochastic optimization.