D-solutions of BSDEs with Poisson jumps

TL;DR

This paper proves the existence and uniqueness of solutions for backward stochastic differential equations with jumps driven by Brownian motion and Poisson random measure under minimal integrability conditions.

Contribution

It establishes the first general existence and uniqueness results for BSDEs with jumps in a broad filtration with minimal assumptions.

Findings

Unique solutions exist for BSDEs with jumps under integrability conditions.

Solutions belong to class D, ensuring certain regularity.

The results extend previous work to more general filtrations.

Abstract

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admits a unique solution which belongs to class D.