Doubly reflected generalized BSDEs with two completely separated RCLL barriers in a general filtration

Abstract In this paper, we investigate doubly reflected generalized backward stochastic differential equations with two reflecting right-continuous with left-limited barriers in a general filtration supporting a Brownian motion and an independent integer-valued random measure. We establish the existence and uniqueness of the solution when the barriers and their left limits are completely separated without assuming Mokobodski’s hypothesis or the regularity condition.