Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

TL;DR

This paper studies a new class of mean-field anticipated backward stochastic differential equations driven by fractional Brownian motion, establishing their existence, uniqueness, comparison theorem, and applying them to stochastic control problems.

Contribution

It introduces and analyzes a novel type of MF-BSDE driven by fractional Brownian motion with H>1/2, including existence, uniqueness, and comparison results, and applies them to control problems.

Findings

Existence and uniqueness of the new MF-BSDEs are proven.

A comparison theorem for these MF-BSDEs is established.

A stochastic optimal control problem is solved using these equations.

Abstract

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of BSDEs are established using two different approaches. Then, a comparison theorem for such BSDEs is obtained. Finally, as an application of this type of equations, a related stochastic optimal control problem is studied and the related sufficient maximum principle is obtained.