Reflected BSDEs with default time and irregular obstacles

Badr Elmansouri

doi:10.5802/crmath.713

Research article - Probability theory

Reflected BSDEs with default time and irregular obstacles

Badr Elmansouri ¹

¹ Laboratory of Analysis and Applied Mathematics (LAMA), Faculty of Sciences Agadir, Ibn Zohr University, BP 8106-Cité Dakhla, 80000, Agadir, Morocco

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 223-233.

Abstract (Original language)
Résumé

In this note, we study reflected backward stochastic differential equations with a default time, where the reflecting obstacle is not necessarily right-continuous. We establish the existence and uniqueness of a solution for such equations under a stochastic Lipschitz condition on the coefficient.

Dans cette note, nous étudions les équations différentielles stochastiques rétrogrades réfléchies avec un temps de défaut, où l’obstacle de réflexion n’est pas nécessairement continu à droite. Nous établissons l’existence et l’unicité d’une solution pour de telles équations sous une condition de Lipschitz stochastique sur le coefficient.

Received: 2024-08-01
Revised: 2024-12-14
Accepted: 2024-12-16
Published online: 2025-04-08

DOI: 10.5802/crmath.713

Classification: 60H05, 60H30, 60G40, 91G80
Keywords: Reflected BSDEs, irregular obstacle, stochastic Lipschitz coefficient, Mertens decomposition
Mots-clés : EDSRs réfléchies, obstacle irrégulier, coefficient de Lipschitz stochastique, décomposition de Mertens

Author's affiliations:

Badr Elmansouri ¹

¹ Laboratory of Analysis and Applied Mathematics (LAMA), Faculty of Sciences Agadir, Ibn Zohr University, BP 8106-Cité Dakhla, 80000, Agadir, Morocco

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Badr Elmansouri},
     title = {Reflected {BSDEs} with default time and irregular obstacles},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {223--233},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2025},
     doi = {10.5802/crmath.713},
     language = {en},
}

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Badr Elmansouri. Reflected BSDEs with default time and irregular obstacles. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 223-233. doi : 10.5802/crmath.713. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.713/

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