Comptes Rendus
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

Ying Hu1 ; Shige Peng2
1 IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France
2 Institute of Mathematics, Shandong University, Jinan, 250100, China
Comptes Rendus. Mathématique, Volume 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
Ying Hu 1 ; Shige Peng 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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Ying Hu; Shige Peng. On the comparison theorem for multidimensional BSDEs. Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 135-140. doi : 10.1016/j.crma.2006.05.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.019/

[1] P. Briand; F. Coquet; Y. Hu; J. Memin; S. Peng A converse comparison theorem for BSDEs and related properties of g-expectation, Electron. Comm. Probab., Volume 5 (2000), pp. 101-117

[2] R. Buckdahn; M. Quincampoix; A. Rascanu Viability property for a backward stochastic differential equation and applications to partial differential equations, Probab. Theory Related Fields, Volume 116 (2000), pp. 485-504

[3] F. Coquet; Y. Hu; J. Memin; S. Peng 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] N. El Karoui; S. Peng; M.C. Quenez Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997), pp. 1-71

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

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