Doubly Reflected Backward Stochastic Differential Equations in the Predictable Setting

Ihsan Arharas (), Siham Bouhadou () and Youssef Ouknine ()
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Ihsan Arharas: Cadi Ayyad University
Siham Bouhadou: Cadi Ayyad University
Youssef Ouknine: Cadi Ayyad University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 115-141

Abstract: 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.

Keywords: Doubly reflected backward stochastic differential equations; Predictable DRBSDEs; Non-quasi-left continuous; Picard iteration method; Fixed point theorem; 60H20; 60H30; 65C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01070-5

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