[EDSR avec le temps aléatoire de défaut et les jeux associés différentiels stochastiques à somme nulle]
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.
Accepté le :
Publié le :
Shige Peng 1 ; Xiaoming Xu 1
@article{CRMATH_2010__348_3-4_193_0,
author = {Shige Peng and Xiaoming Xu},
title = {BSDEs with random default time and related zero-sum stochastic differential games},
journal = {Comptes Rendus. Math\'ematique},
pages = {193--198},
publisher = {Elsevier},
volume = {348},
number = {3-4},
year = {2010},
doi = {10.1016/j.crma.2009.11.009},
language = {en},
}
TY - JOUR AU - Shige Peng AU - Xiaoming Xu TI - BSDEs with random default time and related zero-sum stochastic differential games JO - Comptes Rendus. Mathématique PY - 2010 SP - 193 EP - 198 VL - 348 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2009.11.009 LA - en ID - CRMATH_2010__348_3-4_193_0 ER -
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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