Multi-dimensional reflected McKean-Vlasov BSDEs with the obstacle depending on both the first unknown and its distribution
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 and its distribution . 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.
Keywords
Cite
@article{arxiv.2309.10427,
title = {Multi-dimensional reflected McKean-Vlasov BSDEs with the obstacle depending on both the first unknown and its distribution},
author = {Ruisen Qian},
journal= {arXiv preprint arXiv:2309.10427},
year = {2023}
}