Doubly Reflected Backward Stochastic Differential Equations in the Predictable Setting


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Output type: Journal article

UM6P affiliated Publication?: Yes

Author list: Arharas, Ihsan; Bouhadou, Siham; Ouknine, Youssef

Publisher: Springer Verlag (Germany)

Publication year: 2021

Journal: Journal of Theoretical Probability (0894-9840)

ISSN: 0894-9840

eISSN: 1572-9230

Languages: English (EN-GB)


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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 Ito'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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Last updated on 2021-15-06 at 23:20