A maximum principle for stochastic optimal control with terminal state constraints, and its applications. (English) Zbl 1132.93050

Ji, Shaolin; Zhou, Xun Yu

Commun. Inf. Syst. 6, No. 4, 321-338 (2006).

Summary: 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.

MSC:

93E20	Optimal stochastic control
49K45	Optimality conditions for problems involving randomness

Keywords:

forward-backward stochastic differential equation (FBSDE); state constraints; Ekeland’s variational principle; maximum principle; recursive utility; linear-quadratic control