Existence and uniqueness for $\mathbb{D}$-solutions of reflected BSDEs with two barriers without Mokobodzki's condition

Imen  Hassairi

doi:10.3934/cpaa.2016.15.1139

Article Contents

2016, Volume 15, Issue 4: 1139-1156. Doi: 10.3934/cpaa.2016.15.1139

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Existence and uniqueness for $\mathbb{D}$-solutions of reflected BSDEs with two barriers without Mokobodzki's condition

Imen Hassairi^1,

1.
Université de Sfax, Faculté des Sciences de Sfax, département de mathématiques, BP 1171 Sfax 3000

Received: December 31, 2014

Revised: January 31, 2016

Published: June 2016

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Abstract

In this paper, we are interested in the problem of existence and uniqueness of a solution which belongs to class $\mathbb{D}$ for a backward stochastic differential equation with two strictly separated continuous reflecting barriers in the case when the data are $\mathbb{L}^1$-integrable and with generator satisfying the Lipschitz property. The main idea is to use the notion of local solution to obtain the global one.

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Mathematics Subject Classification: Primary: 60G40, 60H20, 60F25.

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