Particles Systems for Mean Reflected BSDEs

TL;DR

This paper extends the theory of mean reflected backward stochastic differential equations (BSDEs) by developing particle system methods, analyzing convergence rates, and handling general and linear reflection cases.

Contribution

It introduces particle system approaches for mean reflected BSDEs and establishes convergence rates, extending prior work to backward equations with general and linear reflection.

Findings

Established convergence rates of particle systems to mean reflected BSDE solutions.

Extended chaos propagation techniques to backward stochastic equations.

Handled both general and linear reflection cases in the particle framework.

Abstract

In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in [3]. We extend the recent work [2] of Briand, Chaudru de Raynal, Guillin and Labart on the chaos propagation for mean reflected SDEs to the backward framework. When the driver does not depend on z, we are able to treat general reflexions for the particles system. We consider linear reflexion when the driver depends also on z. In both cases, we get the rate of convergence of the particles system towards the square integrable deterministic flat solution to the mean reflected BSDE.