Anticipative backward stochastic differential equations driven by fractional Brownian motion

TL;DR

This paper investigates anticipative backward stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/2, establishing existence, uniqueness, and comparison results using divergence operator integrals.

Contribution

It introduces a framework for solving anticipative BSDEs driven by fractional Brownian motion with H>1/2, including existence, uniqueness, and comparison theorems.

Findings

Existence and uniqueness of solutions for anticipative BSDEs with fractional Brownian motion.

Development of a comparison theorem for these anticipative BSDEs.

Application of divergence operator type integrals in the analysis.

Abstract

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence operator type integral. We obtain the existence and uniqueness of solutions to these equations. A comparison theorem for this type of anticipative BSDEs is also established.