Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator release_5oknpl2345gwhbpgtnz6eml7ju

by Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song

Published in Boundary Value Problems by Springer Science and Business Media LLC.

2024   Volume 2024, Issue 1

Abstract

<jats:title>Abstract</jats:title>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.
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