Doubly Reflected BSDEs in the predictable setting

2019/08/21 by Arharas, Ihsan, Bouhadou, Siham, Ouknine, Youssef
#60H20 #60H30 #65C30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1908.08076

Abstract

In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration 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 fixed point theorem. By using an appropriate generalization of Itô's formula due to Gal'chouk and Lenglart, we provide a suitable a priori estimates which immediately implies the uniqueness of the solution.

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