GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS*

doi:10.1007/s10473-023-0518-4

Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (5): 2234-2262.doi: 10.1007/s10473-023-0518-4

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GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS^*

Junsong LI¹, Chao MI¹, Chuanzhi XING^2†, Dehao ZHAO¹

1. School of Mathematics and Statistics, Shandong University, Weihai 264209, China;
2. Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations, Ministry of Education, Shandong University, Qingdao 266237, China

Received:2021-09-28 Revised:2023-04-08 Online:2023-10-26 Published:2023-10-25
Contact: †Chuanzhi XING, E-mail: xingchuanzhi@sdu.edu.cn;
About author:Junsong LI, E-mail: junsongli@mail.sdu.edu.cn; Chao MI, E-mail: mihchao94@mail.sdu.edu.cn; Dehao ZHAO, E-mail: zhaodehao@mail.sdu.edu.cn
Supported by:
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).

Abstract

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.

Key words: reflected backward stochastic differential equations, forward-backward stochastic differential equations, comparison theorem, Wasserstein metric, mean-field

CLC Number:

60H10

Junsong LI, Chao MI, Chuanzhi XING, Dehao ZHAO. GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS^*[J].Acta mathematica scientia,Series A, 2023, 43(5): 2234-2262.

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GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS^*

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