$\boldsymbol{\mathbb{L}^p(p\ge2)}$-solutions of generalized BSDEs with jumps and monotone generator in a general filtration

M'hamed Eddahbi; Imade Fakhouri; Youssef Ouknine

doi:10.15559/17-VMSTA73

paper

$L^{p} (p \geq 2)$ -solutions of generalized BSDEs with jumps and monotone generator in a general filtration

arXiv:1704.02132 · doi:10.15559/17-VMSTA73

Abstract

In this paper, we study multidimensional generalized BSDEs that have a monotone generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. First, we prove the existence and uniqueness of $L^{p} (p \geq 2)$ -solutions in the case of a fixed terminal time under suitable $p$ -integrability conditions on the data. Then, we extend these results to the case of a random terminal time. Furthermore, we provide a comparison result in dimension $1$ .

Published at http://dx.doi.org/10.15559/17-VMSTA73 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

Lp(p≥2)-solutions of generalized BSDEs with jumps and monotone generator in a general filtration

Abstract

$L^{p} (p \geq 2)$ -solutions of generalized BSDEs with jumps and monotone generator in a general filtration