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

Abstract

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. Since the existing bounded mean oscillation (BMO) martingale approach used in the setting of quadratic BSDEs with bounded terminal conditions is not directly applicable to the present setting, we introduce a new probability measure, under which all subsequent analysis is then carried out. Finally, a global stochastic maximum principle is obtained.