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

TL;DR

This paper studies mean-field backward stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/2, establishing their existence, uniqueness, and a comparison theorem, and linking them to nonlocal PDEs.

Contribution

It introduces the first existence, uniqueness, and comparison results for mean-field BSDEs driven by fractional Brownian motion with H > 1/2, and connects these equations to nonlocal PDEs.

Findings

Existence and uniqueness of solutions under Lipschitz conditions

Comparison theorem for mean-field BSDEs driven by fractional Brownian motion

Connection between mean-field BSDEs and nonlocal PDEs

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).