Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion

In this paper, we study a coupled forward-backward stochastic control system driven by G-Brownian motion. Based on some detailed estimates for control system, we obtain the variational inequality for cost functional, which is a necessary condition for optimality. Furthermore, we prove that this necessary condition is also a sufficient condition under the usual convexity assumptions.