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General Coupled Mean-Field Reflected Forward-Backward Stochastic Differential Equations

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Abstract

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations (FBSDEs), whose coefficients not only depend on the solution but also on the law of the solution. The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations (BSDEs) under Lipschitz conditions, and for the one-dimensional case a comparison theorem is studied. With the help of this comparison result, we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions. It should be mentioned that, under appropriate assumptions, we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University, Weihai, 264209, China

    Junsong Li, Chao Mi & Dehao Zhao

  2. Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations, Ministry of Education, Shandong University, Qingdao, 266237, China

    Chuanzhi Xing

Authors
  1. Junsong Li
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  2. Chao Mi
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  3. Chuanzhi Xing
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  4. Dehao Zhao
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Correspondence to Chuanzhi Xing.

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Conflict of Interest

The authors declare no conflict of interest.

The work was supported in part by the NSFC (11871037), Shandong Province (JQ201202), NSFC-RS (11661130148; NA150344), 111 Project (B12023). Chuanzhi Xing’s research was supported by the Qingdao Postdoctoral Application Research Project (QDBSH20220202092).

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Li, J., Mi, C., Xing, C. et al. General Coupled Mean-Field Reflected Forward-Backward Stochastic Differential Equations. Acta Math Sci 43, 2234–2262 (2023). https://doi.org/10.1007/s10473-023-0518-4

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  • DOI: https://doi.org/10.1007/s10473-023-0518-4

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