Anticipated BSDEs driven by fractional Brownian motion with a time-delayed generator
Document Type
Article
Publication Date
12-1-2023
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 is an element of(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.
Keywords
Anticipated, BSDE, Fractional Brownian motion, Delayed generator, Comparison theorem
Divisions
MathematicalSciences
Funders
Scientific research projects in Anhui universities
Publication Title
Mathematics
Volume
11
Issue
23
Publisher
MDPI
Publisher Location
ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND