Particles Systems and Numerical Schemes for Mean Reflected Stochastic Differential Equations

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.