A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition

In this paper, we study a stochastic optimal control problem for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition, where the control domain is not necessarily convex. Due to the absence of bounded mean oscillation (BMO) martingales approach, we introduce a new probability measure, under which all subsequent analysis is then carried out under this new measure. Finally, by means of a new approach to the derivation of the adjoint equations, a global stochastic maximum principle is established.