Maximum principle for forward–backward stochastic control system under GG-expectation and relation to dynamic programming

In this paper, based on the theory of stochastic differential equations on a sublinear expectation space (Ω,H,Eˆ), we develop a stochastic maximum principle for a general forward–backward stochastic control system under GG-expectation. Under some convexity assumptions, we also obtain sufficient conditions for the optimality. Furthermore, relations between the adjoint processes and the value function for stochastic recursive optimal control problems are given. Finally, applications of our main results to the recursive utility portfolio optimization problem in financial market are discussed.