Reflected BSDEs with default time and irregular obstacles

Badr Elmansouri

doi:10.5802/crmath.713

Article de recherche - Probabilités

Reflected BSDEs with default time and irregular obstacles
[EDSRs réfléchies avec temps de défaut et obstacles irréguliers]

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.

Résumé
Abstract

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.

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.

Reçu le : 2024-08-01
Révisé le : 2024-12-14
Accepté le : 2024-12-16
Publié le : 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

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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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},
     volume = {363},
     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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