Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator

Abstract Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this pape...

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Bibliographic Details
Published in:Boundary Value Problems
Main Authors: Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song
Format: Article
Language:English
Published: SpringerOpen 2024-03-01
Subjects:
Fractional backward stochastic differential equations
Caputo
Fractional Brownian motion
Time-delay generator
Online Access:https://doi.org/10.1186/s13661-024-01842-6
Description
Summary:Abstract Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to conventional BSDEs, in this class of equations, the generator is also affected by the past values of solutions. Under the Lipschitz condition and some new assumptions, we present a theorem on the existence and uniqueness of solutions.
ISSN:1687-2770

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