$L^p$ Solutions of Backward Stochastic Differential Equations with Jumps

Abstract

Given $p\in (1,2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)-$variables. We show that such a BSDEJ with a p-integrable terminal data admits a unique $L^p$ solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.

Keywords: Backward stochastic differential equations with jumps, $L^p$ solutions, monotonic generators, convolution with mollifiers