Comptes Rendus
no. 9
Probability Theory
A generalized existence theorem of BSDEs
[Un théorème d'existence généralisé des EDSRs]

Présenté par : Paul Malliavin

Guangyan Jia1
1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, P.R. China
Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 685-688.

Dans cette Note, nous traitons l'équation différentielle stochastique rétrograde en une dimension, où le coéfficient est Lipschitzien à gauche en y (peut-être discontinu) et Lipschitzien en z, sans croissance contrainte explicite. Nous montrons, dans ce cas, un théorème d'existence de la solution pour équation différentielle stochastique rétrograde.

In this Note, we deal with one-dimensional backward stochastic differential equations (BSDEs) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z, but without explicit growth constraint. We prove, in this setting, an existence theorem for backward stochastic differential equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.02.020
Guangyan Jia 1

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, P.R. China 
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Guangyan Jia. A generalized existence theorem of BSDEs. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 685-688. doi : 10.1016/j.crma.2006.02.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.020/

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

[2] M. Kobylanski Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab., Volume 28 (2000), pp. 259-276

[3] J.P. Lepeltier; J.S. Martin Backward stochastic differential equations with continuous coefficients, Statist. Probab. Lett., Volume 34 (1997), pp. 425-430

[4] E. Pardoux Backward stochastic differential equations and viscosity solutions, Stochastic Analysis and Related Topics, vol. VI, Birkhäuser, 1996, pp. 79-128

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

[6] S. Peng Nonlinear expectations, nonlinear evaluations and risk measures (M. Frittelli; W. Runggaldier, eds.), Stochastic Methods in Finance, Lecture Notes in Math., vol. 1856, Springer-Verlag, Berlin, 2004, pp. 165-253

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