A global stochastic maximum principle for delayed forward-backward stochastic control systems

In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is obtained by using a new method. More precisely, this method introduces first-order and second-order auxiliary equations and offers a novel approach to deriving the adjoint equations as well as the variational equation for $y^{\text{e}}-y^{\ast }$.