Comptes Rendus
no. 7
Probability Theory
Some results on the uniqueness of generators of backward stochastic differential equations
[Quelques résultats sur l'unicité des générateurs des équations différentielles stochastiques rétrogrades]

Présenté par : Paul Malliavin

Long Jiang1, 2
1 Department of Mathematics, Shandong University, 250100 Jinan, China
2 Department of Mathematics, China University of Mining and Technology, 221008 Xuzhou, China
Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 575-580.

L'auteur prouve que le générateur g d'une équation différentielle stochastique rétrograde peut être déterminé uniquement par les valeurs initiales d'équation différentielle stochastique rétrograde correspondante avec toutes les conditions terminales. Le résultat principal confirme et étend le résultat de Peng.

It is proved that the generator g of a backward stochastic differential equation (BSDE) can be uniquely determined by the initial values of the corresponding BSDEs with all terminal conditions. The main results also confirm and extend Peng's conjecture.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.01.026
Long Jiang 1, 2

1 Department of Mathematics, Shandong University, 250100 Jinan, China
2 Department of Mathematics, China University of Mining and Technology, 221008 Xuzhou, China 
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Long Jiang. Some results on the uniqueness of generators of backward stochastic differential equations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 575-580. doi : 10.1016/j.crma.2004.01.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.01.026/

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

[2] Z. Chen A Property of backward stochastic differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 326 (1998) no. 4, pp. 483-488

[3] Z. Chen; L. Epstein Ambiguity, risk and asset returns in continuous time, Econometrica, Volume 70 (2002), pp. 1403-1443

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

[5] N. El Karoui; S. Peng; M.C. Quenez Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997) no. 1, pp. 1-71

[6] E. Pardoux; S. Peng Adapted solution of a backward stochastic differential equation, Systems Control Lett., Volume 14 (1990), pp. 55-61

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