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

Ruisen Qian

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arXiv · 2309.10427

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

Ruisen Qian

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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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Ruisen Qian. 2023-09-19. Multi-dimensional reflected McKean-Vlasov BSDEs with the obstacle depending on both the first unknown and its distribution. https://arxiv.org/abs/2309.10427

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