Comptes Rendus
no. 15-16
Probability Theory/Numerical Analysis
Numerical solutions of backward stochastic differential equations: A finite transposition method
[Solutions numériques des équations différentielles stochastiques rétrogrades : « A finite transposition method »]

Présenté par : Philippe G. Ciarlet

Penghui Wang1 ; Xu Zhang2, 3
1 School of Mathematics, Shandong University, Jinan 250100, China
2 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3 Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China
Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 901-903.

Dans cette Note, nous présentons une nouvelle méthode pour résoudre numériquement les équations différentielles stochastiques rétrogrades. Notre méthode ressemble à la méthode des éléments finis qui permet de résoudre numériquement les équations aux dérivées partielles déterministes.

In this Note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.011
Penghui Wang 1 ; Xu Zhang 2, 3

1 School of Mathematics, Shandong University, Jinan 250100, China
2 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3 Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China 
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     title = {Numerical solutions of backward stochastic differential equations: {A} finite transposition method},
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Penghui Wang; Xu Zhang. Numerical solutions of backward stochastic differential equations: A finite transposition method. Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 901-903. doi : 10.1016/j.crma.2011.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.011/

[1] J.-M. Bismut, Analyse convexe et probabilitiés, PhD thesis, Faculté des Sciences de Paris, Paris, France, 1973.

[2] B. Bouchard; R. Elie; N. Touzi Discrete-time approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs, Radon Ser. Comp. Appl. Math., Volume 8 (2009), pp. 1-34

[3] P.G. Ciarlet The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978

[4] R. Ghanem; P. Spanos Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, 1991

[5] M. Kleiber; T.D. Hien The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation, John Wiley, 1992

[6] Q. Lü; X. Zhang Well-posedness of backward stochastic differential equations with general filtration (preprint, see) | arXiv

[7] J. Ma; P. Protter; J. San Martin; S. Rorres Numerical method for backward stochastic differential equations, Ann. Appl. Probab., Volume 12 (2000), pp. 302-316

[8] A. Nouy Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations, Arch. Comput. Methods Eng., Volume 16 (2009), pp. 251-285

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

[10] S. Peng; M. Xu Numerical algorithms for 1-d backward stochastic differential equations: convergence and simulations, ESAIM: M2AN, Volume 45 (2011), pp. 335-360

[11] P. Wang, X. Zhang, Numerical analysis on backward stochastic differential equations by a finite transposition method, preprint.

[12] J. Zhang A numerical scheme for BSDEs, Ann. Appl. Probab., Volume 14 (2004), pp. 459-488

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