Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Abstract

We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu \cite{PX2009} 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. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.