Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales

TL;DR

This paper establishes fundamental theorems on existence, uniqueness, and comparison for backward stochastic differential equations driven by multi-dimensional RCLL martingales, broadening the framework for nonlinear financial models with jumps.

Contribution

It develops a general multi-asset framework for BSDEs driven by RCLL martingales, extending previous models involving Brownian motion and single-jump martingales.

Findings

Proves existence and uniqueness of solutions for the BSDEs.

Establishes strict comparison theorems for solutions.

Provides a unified approach for multi-asset nonlinear financial models.

Abstract

Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models with jumps, including as particular cases the setups studied by Peng and Xu \cite{PX2009,PX2010} and Dumitrescu et al. \cite{DGQS2018} who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.