Mean‐field backward stochastic differential equations driven by G ‐Brownian motion and related partial differential equations

In this paper, we study mean‐field backward stochastic differential equations driven by G ‐Brownian motion ( G ‐BSDEs). We first obtain the existence and uniqueness theorem of these equations. In fact, we can obtain local solutions by constructing Picard contraction mapping for Y term on small interval, and the global solution can be obtained through backward iteration of local solutions. Then, a comparison theorem for this type of mean‐field G ‐BSDE is derived. Furthermore, we establish the connection of this mean‐field G ‐BSDE and a nonlocal partial differential equation. Finally, we give an application of mean‐field G ‐BSDE in stochastic differential utility model.