Approximation scheme for solutions of backward stochastic differential equations via the representation theorem
El Otmani, Mohamed
Annales mathématiques Blaise Pascal, Tome 13 (2006), p. 17-29 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

@article{AMBP_2006__13_1_17_0,
     author = {El Otmani, Mohamed},
     title = {Approximation scheme for solutions of backward stochastic differential equations via the representation theorem},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     year = {2006},
     pages = {17-29},
     doi = {10.5802/ambp.212},
     zbl = {1134.60349},
     mrnumber = {2233010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2006__13_1_17_0}
}

El Otmani, Mohamed. Approximation scheme for solutions of backward stochastic differential equations via the representation theorem. Annales mathématiques Blaise Pascal, Tome 13 (2006) pp. 17-29. doi : 10.5802/ambp.212. http://gdmltest.u-ga.fr/item/AMBP_2006__13_1_17_0/

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

[2] Bouchard, B.; Ekeland, I.; Touzi, N. On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance Stoch, Tome 111 (2) (2004), pp. 175-206 | MR 2056536 | Zbl 1071.60059

[3] Bouchard, B.; Touzi, N. Discrete time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, Tome 8 (1) (2004), pp. 45-71 | MR 2056536 | Zbl 1071.60059

[4] Carriére, J.F. Valuation of the early-exercise price for option using simulations and nonparametric regression, Insurance:Mathematics and Economics, Tome 19 (1996), pp. 19-30 | Article | MR 1439613 | Zbl 0894.62109

[5] Chevance, D.; Rogers, L.C.G.; Talay, D Numerical methods for backward stochastic differential equations, Numerical methods in finance, Cambridge University Press (1997), pp. 232-244 | MR 1470517 | Zbl 0898.90031

[6] Cvitanic, J.; Karatzas, I. Backward stochastic differential equations with reflection and Dynkin games, The Annals of Probability, Tome 24 (1996), pp. 2024-2056 | Article | MR 1415239 | Zbl 0876.60031

[7] Douglas, J.; Ma, J.; Protter, P. Numerical methods for forward-backward stochastic differential equations, Annals of Applied Probability, Tome 6 (1996), pp. 940-968 | Article | MR 1410123 | Zbl 0861.65131

[8] El Karoui, N.; Peng, S.; Quenez, Mc. Backward stochastic differential equations in finance, Mathematical Finance (1997), pp. 1-71 | Article | MR 1434407 | Zbl 0884.90035

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

[10] Gobet, E.; Lemor, J.P.; Warin, X. A regression-based Monte-Carlo method to solve backward stochastic differential equations, Annals of Applied Probability, Tome 15(3) (2005), p. 2172-2002 | Article | MR 2152657 | Zbl 02226941

[11] Hamadène, S.; Lepeltier, J-P Zero-sum stochastic differential games and BSDEs, Systems and Control letters, Tome 24 (1995), pp. 259-263 | Article | MR 1321134 | Zbl 0877.93125

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

[13] Ma, J.; Protter, P.; Young, J. Solving forward backward stochastic differential equations explicitly: a four step scheme, Probability Theory and Related Fields, Tome 98 (1994), pp. 339-359 | Article | MR 1262970 | Zbl 0794.60056

[14] Ma, J.; Zhang, J. Representation theorems for backward stochastic differential equations, The Annals of Applied Probability, Tome 12(4) (2002), pp. 1390-1418 | MR 1936598 | Zbl 1017.60067

[15] Ma, J.; Zhang, J. Representation and regularities for solutions to BSDE’s with reflections, Stochastic Processes and their Applications, Tome 115 (2005), pp. 539-569 | Article | MR 2152246 | Zbl 1076.60049

[16] Pardoux, E.; Peng, S. Adapted solution of backward stochastic differential equations, Systems and control Letters, Tome 14 (1990), pp. 51-61 | Article | Zbl 0692.93064

[17] Zhang, J. A numerical scheme for BSDE’s, The Annals of Applied Probability, Tome 14(1) (2004), pp. 459-488 | Article | Zbl 1056.60067