$L^p$-Solutions and Comparison Results for L\'evy Driven BSDEs in a Monotonic, General Growth Setting

TL;DR

This paper develops a unified framework for $L^p$-solutions of multidimensional Lévy-driven BSDEs with general growth and monotonicity conditions, extending previous results and establishing new existence, uniqueness, and comparison theorems.

Contribution

It introduces a generalized approach to $L^p$-solutions for Lévy-driven BSDEs under broader conditions, extending prior work in the field.

Findings

Established new existence and uniqueness results.

Proved comparison theorems under extended monotonicity conditions.

Generalized previous results to more complex growth and filtration settings.

Abstract

We present a unified approach to $L^p$-solutions ($p > 1$) of multidimensional backward stochastic differential equations (BSDEs) driven by L\'evy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the $y$-variable and have general growth in $y$. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008), Yao (2017), Kruse and Popier (2016/2017) and Geiss and Steinicke (2018).