Stochastic Maximum Principle For Fully Coupled Mean-field Forward-backward Stochastic Control System With Terminal State Constrains

In this paper,we consider an optimal control problem with terminal state constrains,where the control system is described by a fully coupled mean-field forwardbackward stochastic differential equation.The terminal state of the forward equation in the control system is limited in a convex set.First,by using the mean-field backward stochastic differential equation theory and the terminal perturbation approach,we get the equivalent form of the control system.We solve the difficulty arising from the diffusion term depending on the control variable in the optimal control problem.Then we adopt the Ekeland's variational principle to deal with the state constraints in order to obtain the stochastic maximum principle,which characterizes the necessary conditions of the optimal control.Finally,the stochastic linear quadratic control problem with terminal state constraints is discussed.