L^p -solution for BSDEs with jumps in the case p \textless{} 2. Corrections to the paper "BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration"

TL;DR

This paper corrects previous results on the existence and uniqueness of solutions to backward stochastic differential equations with jumps for p less than 2, removing some earlier assumptions and providing a revised proof.

Contribution

It provides a corrected proof for L^p solutions of BSDEs with jumps when p<2 and removes the quasi-left continuity condition on the filtration.

Findings

Corrected proof for BSDE solutions in L^p for p<2

Removal of the quasi-left continuity condition

Clarification of existence and uniqueness under monotonicity

Abstract

In [8] we established existence and uniqueness of solutions of backward stochastic differential equations in L^p under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case 1 \textless{} p \textless{} 2. Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.