Reflected BSDEs Driven by RCLL Martingales with Stochastic Lipschitz Coefficient in a General Filtration: Analysis and Applications

Abstract

In this paper, we investigate reflected backward stochastic differential equations with a single, discontinuous barrier, driven by a right-continuous, left-limited martingale within a general filtration. We establish the existence and uniqueness of solutions under a stochastic Lipschitz condition on the generator and a reflection process that is right-continuous with left limits. As an application, we use these results to determine fair pricing for American contingent claim options in a financial market driven by Azéma’s martingale, incorporating elements of asymmetric information.