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Mean-Field Backward Stochastic Differential Equations Driven by Fractional Brownian Motion

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Abstract

In this paper, we study a new class of equations called mean-field backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H > 1/2. First, the existence and uniqueness of this class of BSDEs are obtained. Second, a comparison theorem of the solutions is established. Third, as an application, we connect this class of BSDEs with a nonlocal partial differential equation (PDE, for short), and derive a relationship between the fractional mean-field BSDEs and PDEs.

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Acknowledgements

The authors would like to thank the anonymous referees for their time and comments.

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Authors and Affiliations

  1. Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, 250100, P. R. China

    Yu Feng Shi

  2. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, P. R. China

    Jia Qiang Wen

  3. Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, P. R. China

    Jie Xiong

Authors
  1. Yu Feng Shi
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  2. Jia Qiang Wen
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  3. Jie Xiong
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Corresponding author

Correspondence to Jia Qiang Wen.

Additional information

Yufeng SHI is supported by the National Key R&D Program of China (Grant No. 2018YFA0703900), the National Natural Science Foundation of China (Grant Nos. 11871309 and 11371226). Jiaqiang WEN is supported by China Postdoctoral Science Foundation (Grant No. 2019M660968) and Southern University of Science and Technology Start up fund Y01286233. Jie XIONG is supported by Southern University of Science and Technology Start up fund Y01286120 and the National Natural Science Foundation of China (Grants Nos. 61873325, 11831010)

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Shi, Y.F., Wen, J.Q. & Xiong, J. Mean-Field Backward Stochastic Differential Equations Driven by Fractional Brownian Motion. Acta. Math. Sin.-English Ser. 37, 1156–1170 (2021). https://doi.org/10.1007/s10114-021-0002-9

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  • DOI: https://doi.org/10.1007/s10114-021-0002-9

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