Annales Mathématiques
Blaise Pascal
no. 1
Approximation scheme for solutions of backward stochastic differential equations via the representation theorem
Mohamed El Otmani1
1 Faculty of Sciences Semlalia Department of Mathematics Cadi Ayyad University BP 2390 Marrakesh MOROCCO
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 17-29.

We are interested in the approximation and simulation of solutions for the backward stochastic differential equations. We suggest two approximation schemes, and we study the 𝕃 2 induced error.

DOI : 10.5802/ambp.212
Mohamed El Otmani 1

1 Faculty of Sciences Semlalia Department of Mathematics Cadi Ayyad University BP 2390 Marrakesh MOROCCO 
@article{AMBP_2006__13_1_17_0,
     author = {Mohamed El Otmani},
     title = {Approximation scheme for solutions of backward stochastic differential equations via the representation theorem},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {17--29},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     number = {1},
     year = {2006},
     doi = {10.5802/ambp.212},
     mrnumber = {2233010},
     zbl = {1134.60349},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.212/}
}
TY  - JOUR
AU  - Mohamed El Otmani
TI  - Approximation scheme for solutions of backward stochastic differential equations via the representation theorem
JO  - Annales mathématiques Blaise Pascal
PY  - 2006
SP  - 17
EP  - 29
VL  - 13
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.212/
DO  - 10.5802/ambp.212
LA  - en
ID  - AMBP_2006__13_1_17_0
ER  - 
%0 Journal Article
%A Mohamed El Otmani
%T Approximation scheme for solutions of backward stochastic differential equations via the representation theorem
%J Annales mathématiques Blaise Pascal
%D 2006
%P 17-29
%V 13
%N 1
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.212/
%R 10.5802/ambp.212
%G en
%F AMBP_2006__13_1_17_0
Mohamed El Otmani. Approximation scheme for solutions of backward stochastic differential equations via the representation theorem. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 17-29. doi : 10.5802/ambp.212. https://ambp.centre-mersenne.org/articles/10.5802/ambp.212/

[1] V. Bally An approximation scheme for BSDEs and applications to control and nonlinear PDE’s, Pitman Research Notes in Mathematics Series (1997) (364, Longman)

[2] B. Bouchard; I. Ekeland; N. Touzi On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance Stoch, Volume 111 (2) (2004), pp. 175-206 | MR | Zbl

[3] B. Bouchard; N. Touzi Discrete time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, Volume 8 (1) (2004), pp. 45-71 | MR | Zbl

[4] J.F. Carriére Valuation of the early-exercise price for option using simulations and nonparametric regression, Insurance:Mathematics and Economics, Volume 19 (1996), pp. 19-30 | DOI | MR | Zbl

[5] D. Chevance; L.C.G. Rogers; D Talay Numerical methods for backward stochastic differential equations, Numerical methods in finance, Cambridge University Press, 1997, pp. 232-244 | MR | Zbl

[6] J. Cvitanic; I. Karatzas Backward stochastic differential equations with reflection and Dynkin games, The Annals of Probability, Volume 24 (1996), pp. 2024-2056 | DOI | MR | Zbl

[7] J. Douglas; J. Ma; P. Protter Numerical methods for forward-backward stochastic differential equations, Annals of Applied Probability, Volume 6 (1996), pp. 940-968 | DOI | MR | Zbl

[8] N. El Karoui; S. Peng; Mc. Quenez Backward stochastic differential equations in finance, Mathematical Finance (1997), pp. 1-71 | DOI | MR | Zbl

[9] O. Faure Simulation du mouvement brownien et des diffusions (1992) (PhD thesis, Ecole Nationale des Ponts et Chaussées)

[10] E. Gobet; J.P. Lemor; X. Warin A regression-based Monte-Carlo method to solve backward stochastic differential equations, Annals of Applied Probability, Volume 15(3) (2005), p. 2172-2002 | DOI | MR | Zbl

[11] S. Hamadène; J-P Lepeltier Zero-sum stochastic differential games and BSDEs, Systems and Control letters, Volume 24 (1995), pp. 259-263 | DOI | MR | Zbl

[12] F. Longstaff; E. Schwartz Valuing american options by simulation: a simple least squares approach, The review of Financial studies, Volume 14(1) (2001), pp. 113-147 | DOI

[13] J. Ma; P. Protter; J. Young Solving forward backward stochastic differential equations explicitly: a four step scheme, Probability Theory and Related Fields, Volume 98 (1994), pp. 339-359 | DOI | MR | Zbl

[14] J. Ma; J. Zhang Representation theorems for backward stochastic differential equations, The Annals of Applied Probability, Volume 12(4) (2002), pp. 1390-1418 | MR | Zbl

[15] J. Ma; J. Zhang Representation and regularities for solutions to BSDE’s with reflections, Stochastic Processes and their Applications, Volume 115 (2005), pp. 539-569 | DOI | MR | Zbl

[16] E. Pardoux; S. Peng Adapted solution of backward stochastic differential equations, Systems and control Letters, Volume 14 (1990), pp. 51-61 | DOI | Zbl

[17] J. Zhang A numerical scheme for BSDE’s, The Annals of Applied Probability, Volume 14(1) (2004), pp. 459-488 | DOI | Zbl

Cité par Sources :