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

被引：0
作者：
Yunze Shao
Junjie Du
Xiaofei Li
Yuru Tan
Jia Song
机构：
[1] Yangtze University,School of Information and Mathematics
[2] Jingzhou University,School of Information Engineering
来源：
Boundary Value Problems | / 2024卷
关键词：
Fractional backward stochastic differential equations; Caputo; Fractional Brownian motion; Time-delay generator;
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摘要：
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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