Propagation of chaos for mean-field reflected BSDEs with jumps

TL;DR

This paper investigates the existence, uniqueness, and convergence of particle systems for mean-field reflected backward stochastic differential equations driven by marked point and Poisson processes, advancing theoretical understanding in stochastic analysis.

Contribution

It establishes well-posedness and convergence rates for MF-RBSDEs driven by marked point and Poisson processes, extending previous results to new stochastic drivers.

Findings

Proved existence and uniqueness of particle systems under Lipschitz conditions.

Established convergence of particle systems to MF-RBSDE solutions.

Derived convergence rates for systems driven by Poisson processes.

Abstract

In this paper, we study a class of mean-field reflected backward stochastic differential equations (MF-RBSDEs) driven by a marked point process and also analyze MF-RBSDEs driven by a Poisson process. Based on a $g$-expectation representation lemma, we give the existence and uniqueness of the particle system of MF-RBSDEs driven by a marked point process under Lipschitz generator conditions and obtain a convergence result of this system. We also establish the well-posedness of the MF-RBSDEs driven by a Poisson process and the convergence rate of the corresponding particle system towards the solution to the MF-RBSDEs driven by a Poisson process under bounded terminal, bounded obstacle conditions.