PARTICLES SYSTEMS AND NUMERICAL SCHEMES FOR MEAN REFLECTED STOCHASTIC DIFFERENTIAL EQUATIONS

Philippe Briand (1) , Paul-Eric Chaudru de Raynal (1) , Arnaud Guillin (2) , Céline Labart (1)

1 LAMA - Laboratoire de Mathématiques
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 [BEH16] 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.

Mots clés: particles system; reflected stochastic differential equations

Domaines: Probabilités [math.PR]

Philippe Briand, Paul-Eric Chaudru de Raynal, Arnaud Guillin, Céline Labart. PARTICLES SYSTEMS AND NUMERICAL SCHEMES FOR MEAN REFLECTED STOCHASTIC DIFFERENTIAL EQUATIONS. The Annals of Applied Probability, 2020, 30 (4), pp.1884-1909. ⟨hal-01421479⟩