BSDEs with random default time and related zero-sum stochastic differential games

Shige Peng; Xiaoming Xu

doi:10.1016/j.crma.2009.11.009

Probability Theory

BSDEs with random default time and related zero-sum stochastic differential games
[EDSR avec le temps aléatoire de défaut et les jeux associés différentiels stochastiques à somme nulle]

Présenté par : Paul Malliavin

Shige Peng ¹ ; Xiaoming Xu ¹

¹ School of Mathematics, Shandong University, Jinan, 250100, China

Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 193-198.

Résumé
Abstract

Dans cette Note, nous considirons les équations différentielles stochastiques rétrogrades avec le temps aléatoire de défaut. Les équations sont dirigées par mouvement brownien ainsi qu'une martingale mutuellement indépendants apparaissant dans un cadre de defaut. Nous montrons que ces équations ont des solutions uniques et un théorème de comparaison pour leurs solutions. Comme une application, nous obtenons une stratégie de point-selle pour le jeu associé différentiel stochastique à somme nulle.

In this Note we are concerned with backward stochastic differential equations with random default time. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions and a comparison theorem for their solutions. As an application, we get a saddle-point strategy for the related zero-sum stochastic differential game problem.

Reçu le : 2009-10-15
Accepté le : 2009-11-17
Publié le : 2010-01-20

DOI : 10.1016/j.crma.2009.11.009

Affiliations des auteurs :

Shige Peng ¹ ; Xiaoming Xu ¹

¹ School of Mathematics, Shandong University, Jinan, 250100, China

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Shige Peng; Xiaoming Xu. BSDEs with random default time and related zero-sum stochastic differential games. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 193-198. doi : 10.1016/j.crma.2009.11.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.009/

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