DOUBLY REFLECTED BSDES IN THE PREDICTABLE SETTING YOUSSEF OUKNINE

IHSAN ARHARAS, SIHAM BOUHADOU AND YOUSSEF OUKNINE

Abstract

In this paper, we introduce a speci c kind of doubly reflected Backward Stochastic Di erential Equations (in short DRBSDEs), de ned on probability spaces equipped with general ltration that is essentially non quasi-left continuous, where the barriers are assumed to be predictable processes. We call these equations predictable DRBSDEs.

Under a general type of Mokobodzki's condition, we show the existence of the solution (in consideration of the driver's nature) through a Picard iteration method and a Banach xed point theorem. By using an appropriate generalization of Ito's formula due to Gal'chouk and Lenglart, we provide a suitable a priori estimates which immediately implies the uniqueness of the solution.