Lp solutions of backward stochastic differential equations with jumps

Given p∈(1,2), we study Lp 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 p-integrable terminal data admits a unique Lp solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.