Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator

Author:

Zhang Pei12ORCID,Ibrahim Adriana Irawati Nur1ORCID,Mohamed Nur Anisah1ORCID

Affiliation:

1. Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia

2. School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China

Abstract

This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H∈(1/2,1). This study expands upon the findings of the anticipated BSDE by considering the scenario when the driver is fractional Brownian motion rather instead of standard Brownian motion. Additionally, the generator incorporates not only the present and future but also the past. We will demonstrate the existence and uniqueness of the solutions to these equations by employing the fixed point theorem. Furthermore, an equivalent comparison theorem is derived.

Funder

Scientific research projects in Anhui universities

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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