Lp Solutions of Backward Stochastic Differential Equations with Jumps

Abstract

Abstract Given p ∈ ( 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 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.