Reflected BSDEs with jumps in time-dependent convex càdlàg domains

Abstract

In the first part of the paper, we study the unique solvability of multidimensional reflected backward stochastic differential equations (RBSDEs) of Wiener–Poisson type with reflection in the inward spatial normal direction of a time-dependent adapted càdlàg convex set D={Dt,t∈[0,T]}. The existence result is obtained by approximating the solutions of this class of RBSDEs by solutions of BSDEs with reflection in discretizations of D, while the uniqueness is established by using Itô’s formula. In the second part of the paper, we show that the solutions of our RBSDEs can be approximated via a non-standard penalization method.