Some results on the uniqueness of generators of backward stochastic differential equations

Long Jiang

doi:10.1016/j.crma.2004.01.026

Probability Theory

Some results on the uniqueness of generators of backward stochastic differential equations

Presented by: Paul Malliavin

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

Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 575-580.

Abstract
Résumé

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.

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.

Received: 2003-06-23
Accepted: 2004-01-08
Published online: 2004-03-16

DOI: 10.1016/j.crma.2004.01.026

Author's affiliations:

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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     author = {Long Jiang},
     title = {Some results on the uniqueness of generators of backward stochastic differential equations},
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     doi = {10.1016/j.crma.2004.01.026},
     language = {en},
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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/

References
Cited by

[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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