no. 2
Probability Theory
On the comparison theorem for multidimensional BSDEs
[Sur le théorème de comparaison pour les équations différentielles stochastiques rétrogrades]

Présenté par : Paul Deheuvels

Hu, Ying1 ; Peng, Shige2
1 IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France
2 Institute of Mathematics, Shandong University, Jinan, 250100, China
Comptes Rendus. Mathématique, Tome 343 (2006) no. 2, pp. 135-140.

Dans cette Note, nous donnons une condition nécessaire et suffisante sous laquelle le théorème de comparaison fonctionne pour les équations différentielles stochastiques rétrogrades (EDSR) multidimensionnelles et pour les EDSR à valeurs matricielles.

In this Note, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional backward stochastic differential equations (BSDEs) and for matrix-valued BSDEs.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.05.019
Hu, Ying 1 ; Peng, Shige 2

1 IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France
2 Institute of Mathematics, Shandong University, Jinan, 250100, China 
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Hu, Ying; Peng, Shige. On the comparison theorem for multidimensional BSDEs. Comptes Rendus. Mathématique, Tome 343 (2006) no. 2, pp. 135-140. doi : 10.1016/j.crma.2006.05.019. http://www.numdam.org/articles/10.1016/j.crma.2006.05.019/

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[3] Coquet, F.; Hu, Y.; Memin, J.; Peng, S. A general converse comparison theorem for backward stochastic differential equations, C. R. Acad. Sci. Paris, Sér. I Math., Volume 333 (2001), pp. 577-581

[4] El Karoui, N.; Peng, S.; Quenez, M.C. Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997), pp. 1-71

[5] Pardoux, E.; Peng, S. Backward stochastic differential equations and quasilinear parabolic partial differential equations, Charlotte, NC, 1991 (Lecture Notes in Control and Inform. Sci.), Volume vol. 176, Springer, Berlin (1992), pp. 200-217

[6] Peng, S. A generalized dynamic programming principle and Hamilton–Jacobi–Bellman equation, Stochastics Stochastics Rep., Volume 38 (1992), pp. 119-134

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