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This paper is concerned with a stochastic optimal control problem where the con- trolled 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 prin- ciple is obtained. Applications to state constrained stochastic linear-quadratic control models and a recursive utility optimization problem are investigated.

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