Stochastic Control Problem With Terminal State Constraints Under G-Expectation

This paper mainly studies the stochastic optimal control problem under g-expect-ation,in which the stochastic controlled system is described by the forward-backward stochastic differential equation,and the forward state is constrained in the convex set at the terminal moment.By using the classical theory of backward differential equation,the control system is transformed from forward backward stochastic differen-tial equation into an equivalent backward form,and the equivalent stochastic control problem is introduced.By using Ekeland variational principle,the maximum principle of stochastic optimal control under g-expectation is obtained.Finally,the maximum principle of linear quadratic stochastic optimal control problem under g-expectation is studied.