A propagation of chaos result for weakly interacting nonlinear Snell envelopes

Abstract: In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and right-continuous and left-limited obstacle, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters both the driver and the lower obstacle. Under mild Lipschitz and integrability conditions on the coefficients, we prove existence and uniqueness of the solution to both the mean-field reflected BSDEs with jumps and the corresponding system of weakly interacting particles and provide a propagation of chaos result for the whole solution $(Y,Z,U,K)$, which requires new technical results due to the dependence of the obstacle on the solution and the presence of jumps.