Mean Reflected Stochastic Differential Equations with Jumps

TL;DR

This paper investigates reflected stochastic differential equations with jumps, focusing on solutions constrained by their law, and extends existing results by proving existence, uniqueness, and numerical approximation methods for these equations.

Contribution

It introduces the study of law-constrained reflected SDEs with jumps, proving existence and uniqueness, and generalizes previous numerical schemes to this new setting.

Findings

Proved existence and uniqueness of solutions.

Extended numerical approximation methods to jump processes.

Generalized previous results to law-constrained reflected SDEs with jumps.

Abstract

This paper is devoted to the study of reflected Stochastic Differential Equations with jumps when the constraint is not on the paths of the solution but acts on the law of the solution. This type of reflected equations have been introduced recently by Briand, Elie and Hu [BEH18] in the context of BSDEs, when no jumps occur. In [BCdRGL16], the authors study a numerical scheme based on particle systems to approximate these reflected SDEs. In this paper, we prove existence and uniqueness of solutions to this kind of reflected SDEs with jumps and we generalize the results obtained in [BCdRGL16] to this context.