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Anticipative backward stochastic differential equations driven by fractional Brownian motion

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  • Wen, Jiaqiang
  • Shi, Yufeng

Abstract

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence operator type integral. We obtain the existence and uniqueness theorem to these equations under the Lipschitz condition. A comparison theorem for this type of anticipative BSDEs is also established.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:118-127
    DOI: 10.1016/j.spl.2016.11.011
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    References listed on IDEAS

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    1. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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    Cited by:

    1. Pei Zhang & Adriana Irawati Nur Ibrahim & Nur Anisah Mohamed, 2023. "Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator," Mathematics, MDPI, vol. 11(23), pages 1-13, December.
    2. 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).
    3. Yu, Xianye, 2019. "Non-Lipschitz anticipated backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    4. 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.

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