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General Mean Reflected Backward Stochastic Differential Equations

Author

Listed:
  • Ying Hu

    (Univ. Rennes, CNRS, IRMAR-UMR 6625)

  • Remi Moreau

    (Univ. Rennes, CNRS, IRMAR-UMR 6625)

  • Falei Wang

    (Shandong University)

Abstract

The present paper is devoted to the study of backward stochastic differential equations (BSDEs) with mean reflection formulated by Briand et al. (Ann Appl Probab 28(1):482–510, 2018). We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of solution term Y. Using a fixed-point argument, BMO martingale theory and the $$\theta $$ θ -method, we establish existence and uniqueness results for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.

Suggested Citation

  • Ying Hu & Remi Moreau & Falei Wang, 2024. "General Mean Reflected Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(1), pages 877-904, March.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01288-z
    DOI: 10.1007/s10959-023-01288-z
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    References listed on IDEAS

    as
    1. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    2. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
    3. Briand, Philippe & Hibon, Hélène, 2021. "Particles Systems for mean reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 253-275.
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