The Optimal Control Problem with State Constraints for Fully Coupled Forward-Backward Stochastic Systems with Jumps

We focus on the fully coupled forward-backward stochastic differential equations with jumps and investigate the associated stochastic optimal control problem (with the nonconvex control and the convex state constraint) along with stochastic maximum principle. To derive the necessary condition (i.e., stochastic maximum principle) for the optimal control, first we transform the fully coupled forward-backward stochastic control system into a fully coupled backward one; then, by using the terminal perturbation method, we obtain the stochastic maximum principle. Finally, we study a linear quadratic model.