A Maximum Principle For Stochastic Optimal Control With Terminal State Constraints

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