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Existence and uniqueness of solution for fully coupled fractional forward–backward stochastic differential equations with delay and anticipated term

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  • Kyong-Il, Ri
  • Myong-Guk, Sin

Abstract

This paper deals with fully coupled fractional forward–backward stochastic differential equations (FBSDEs) with delay and anticipated term. In these equations the coefficients depend on not only the future state but also the past one. We investigate the existence and uniqueness result for such FBSDEs by using the method of continuation. We also obtain a comparison theorem.

Suggested Citation

  • Kyong-Il, Ri & Myong-Guk, Sin, 2024. "Existence and uniqueness of solution for fully coupled fractional forward–backward stochastic differential equations with delay and anticipated term," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223001785
    DOI: 10.1016/j.spl.2023.109954
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    References listed on IDEAS

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    1. Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.
    2. Wen, Jiaqiang & Shi, Yufeng, 2017. "Anticipative backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 118-127.
    3. Lucian Maticiuc & Tianyang Nie, 2015. "Fractional Backward Stochastic Differential Equations and Fractional Backward Variational Inequalities," Journal of Theoretical Probability, Springer, vol. 28(1), pages 337-395, March.
    4. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
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