A maximum principle for stochastic optimal control with terminal state constraints, and its applications

This paper is concerned with a stochastic optimal control problem where the controlled system is described by a forward-backward stochastic differential equation (FBSDE), while the forward state is constrained in a convex set at the terminal time. An equivalent backward control problem is introduced. By using Ekeland's variational principle, a stochastic maximum principle is obtained. Applications to state constrained stochastic linear-quadratic control models and a recursive utility optimization problem are investigated.