Generalized Reflected BSDEs with RCLL Random Obstacles in a General Filtration

Abstract

This paper addresses the existence and uniqueness of solutions to Reflected Generalized Backward Stochastic Differential Equations (GRBSDEs) within a general filtration that supports a Brownian motion and an independent integer-valued random measure. Our study focuses on cases where the given data satisfy appropriate ${\mathbb{L}}^2$-integrability conditions and the coefficients satisfy a monotonicity assumption. Additionally, we establish a connection between the solution and an optimal control problem over the set of stopping times.