Connection between the Adjoint Variables and Value Function for Controlled Fully Coupled FBSDEs: The Global Case

This paper deals with an optimal control problem of fully coupled forward-backward stochastic differential equations (FBSDEs), where the diffusion term does not contain the variable $z$ and the control domain is not necessarily convex. The connection among the adjoint variables and the value function is obtained in terms of the sub- and super-derivatives. It generalizes the result in [W. J. Meng, J. T. Shi, Connection between the adjoint variables and value function for controlled fully coupled FBSDEs: The local case, Proc. 15th International Conference on Control, Automation, Robotics and Vision, pp. 1263–1270, November 18–21, Singapore, 2018].