Multi-dimensional reflected McKean-Vlasov BSDEs with the obstacle depending on both the first unknown and its distribution

2023/09/19 by Ruisen Qian, Qian, Ruisen
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2309.10427

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper studies a multi-dimensional mean-field reflected backward stochastic differential equation (MF-RBSDE) with a reflection constraint depending on both the value process Y and its distribution [Y]. We establish the existence, uniqueness and the stability of the solution of MF-RBSDE. We also investigate the associated interacting particle systems of RBSDEs and prove a propagation of chaos result. Lastly, we investigate the relationship between MF-RBSDE and an obstacle problem for partial differential equations in Wasserstein space within a Markovian framework. Our work provides a connection between the work of Briand et al. (2020) on BSDEs with normal reflection in law and the work of Gegout-Petit and Pardoux (1996) on classical multi-dimensional RBSDEs.

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