Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic control systems.

In this paper, we consider stochastic optimal control problems for fully coupled forward-backward stochastic control systems with a nonconvex control domain. Within the framework of viscosity solution, the relationship between the maximum principle and dynamic programming principle is investigated, and the set inclusions among the value function and the adjoint processes are obtained. Three special cases are studied. In the first case, the value function W is supposed to be smooth. In the second case, the diffusion term {\sigma} of the forward stochastic differential equation does not include the term z. Finally, we study the local case in which the control domain is convex.