Particles Systems and Numerical Schemes for Mean Reflected Stochastic Differential Equations

TL;DR

This paper develops a particle system-based numerical scheme to approximate solutions of mean reflected stochastic differential equations, which constrain the law of the solution rather than the path itself.

Contribution

It introduces a novel particle system approach for approximating mean reflected SDEs, enabling practical numerical solutions for these complex equations.

Findings

Proposes a particle system approximation for mean reflected SDEs

Designs a numerical scheme based on the particle system

Provides convergence analysis of the approximation

Abstract

This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by Briand, Elie and Hu (arXiv:1605.06301) in the context of risk measures. Our main objective is to provide an approximation of solutions to these reflected SDEs with the help of interacting particles systems. This approximation allows to design a numerical scheme for this kind of equations.