Necessary conditions of forward-backward stochastic control system with initial-terminal constraints

This paper discuss a stochastic optimal control problem where the control system is described by fully-coupled forward-backward stochastic differential equation(FBSDE)driven by Itô-lévy process. The control variable v(.) and k
_t
(.) are all contain in the diffusion coefficient σ and g, dominate set is required convex and initial-terminal state is constraint. By using traditional variational technique, necessary condition for optimality in stochastic control system of FBSDE is obtained.