On the comparison theorem for multidimensional BSDEs

Ying Hu; Shige Peng

doi:10.1016/j.crma.2006.05.019

Probability Theory

On the comparison theorem for multidimensional BSDEs

Presented by: Paul Deheuvels

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

Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 135-140.

Abstract
Résumé

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.

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.

Received: 2005-04-07
Accepted: 2006-05-22
Published online: 2006-07-11

DOI: 10.1016/j.crma.2006.05.019

Author's affiliations:

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

@article{CRMATH_2006__343_2_135_0,
     author = {Ying Hu and Shige Peng},
     title = {On the comparison theorem for multidimensional {BSDEs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {135--140},
     publisher = {Elsevier},
     volume = {343},
     number = {2},
     year = {2006},
     doi = {10.1016/j.crma.2006.05.019},
     language = {en},
}

TY  - JOUR
AU  - Ying Hu
AU  - Shige Peng
TI  - On the comparison theorem for multidimensional BSDEs
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 135
EP  - 140
VL  - 343
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2006.05.019
LA  - en
ID  - CRMATH_2006__343_2_135_0
ER  -

%0 Journal Article
%A Ying Hu
%A Shige Peng
%T On the comparison theorem for multidimensional BSDEs
%J Comptes Rendus. Mathématique
%D 2006
%P 135-140
%V 343
%N 2
%I Elsevier
%R 10.1016/j.crma.2006.05.019
%G en
%F CRMATH_2006__343_2_135_0

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/

References
Cited by

[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

Cited by Sources:

Comments - Policy