Mean-field backward stochastic differential equations driven by fractional Brownian motion

Abstract

In this paper, we focus on the mean-field backward stochastic differential equations (BSDEs) driven by a fractional Brownian motion with Hurst parameter H greater then 1/2. First, the existence and uniqueness of these equations are established under Lipschitz condition. Then, a comparison theorem for such mean-field BSDEs is obtained. Finally, as an application, we connect this mean-field BSDE with a nonlocal partial differential equation (PDE).