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Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations

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  • Sin, Myong-Guk
  • Ri, Kyong-Il
  • Kim, Kyong-Hui

Abstract

We study a coupled fractional mean-field forward–backward stochastic differential equation (MF-FBSDE), in which the coefficients involved could also depend upon the distribution of the solution (X, Y), and which contains a special structure η. We prove the existence and uniqueness of a solution of the fractional MF-FBSDE by using the method of continuation.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:190:y:2022:i:c:s0167715222001481
    DOI: 10.1016/j.spl.2022.109608
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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. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    3. 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.
    4. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    5. 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.
    6. Nualart, David & Saussereau, Bruno, 2009. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 391-409, February.
    7. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    8. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.
    9. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    10. Bensoussan, A. & Yam, S.C.P. & Zhang, Z., 2015. "Well-posedness of mean-field type forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3327-3354.
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    Cited by:

    1. 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).

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