Voir la notice de l'article provenant de la source Numdam
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 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}, pages = {17--29}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {13}, number = {1}, year = {2006}, doi = {10.5802/ambp.212}, zbl = {1134.60349}, mrnumber = {2233010}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.5802/ambp.212/} }
TY - JOUR AU - El Otmani, Mohamed 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 - http://geodesic.mathdoc.fr/articles/10.5802/ambp.212/ DO - 10.5802/ambp.212 LA - en ID - AMBP_2006__13_1_17_0 ER -
%0 Journal Article %A El Otmani, Mohamed %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 http://geodesic.mathdoc.fr/articles/10.5802/ambp.212/ %R 10.5802/ambp.212 %G en %F 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) no. 1, pp. 17-29. doi : 10.5802/ambp.212. http://geodesic.mathdoc.fr/articles/10.5802/ambp.212/
[1] An approximation scheme for BSDEs and applications to control and nonlinear PDE’s, Pitman Research Notes in Mathematics Series (1997) (364, Longman)
[2] On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance Stoch, Volume 111 (2) (2004), pp. 175-206 | Zbl | MR
[3] Discrete time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, Volume 8 (1) (2004), pp. 45-71 | Zbl | MR
[4] Valuation of the early-exercise price for option using simulations and nonparametric regression, Insurance:Mathematics and Economics, Volume 19 (1996), pp. 19-30 | DOI | Zbl | MR
[5] Numerical methods for backward stochastic differential equations, Numerical methods in finance, Cambridge University Press, 1997, pp. 232-244 | Zbl | MR
[6] Backward stochastic differential equations with reflection and Dynkin games, The Annals of Probability, Volume 24 (1996), pp. 2024-2056 | DOI | Zbl | MR
[7] Numerical methods for forward-backward stochastic differential equations, Annals of Applied Probability, Volume 6 (1996), pp. 940-968 | DOI | Zbl | MR
[8] Backward stochastic differential equations in finance, Mathematical Finance (1997), pp. 1-71 | DOI | Zbl | MR
[9] Simulation du mouvement brownien et des diffusions (1992) (PhD thesis, Ecole Nationale des Ponts et Chaussées)
[10] A regression-based Monte-Carlo method to solve backward stochastic differential equations, Annals of Applied Probability, Volume 15(3) (2005), p. 2172-2002 | DOI | Zbl | MR
[11] Zero-sum stochastic differential games and BSDEs, Systems and Control letters, Volume 24 (1995), pp. 259-263 | DOI | Zbl | MR
[12] Valuing american options by simulation: a simple least squares approach, The review of Financial studies, Volume 14(1) (2001), pp. 113-147 | DOI
[13] Solving forward backward stochastic differential equations explicitly: a four step scheme, Probability Theory and Related Fields, Volume 98 (1994), pp. 339-359 | DOI | Zbl | MR
[14] Representation theorems for backward stochastic differential equations, The Annals of Applied Probability, Volume 12(4) (2002), pp. 1390-1418 | Zbl | MR
[15] Representation and regularities for solutions to BSDE’s with reflections, Stochastic Processes and their Applications, Volume 115 (2005), pp. 539-569 | DOI | Zbl | MR
[16] Adapted solution of backward stochastic differential equations, Systems and control Letters, Volume 14 (1990), pp. 51-61 | DOI | Zbl
[17] A numerical scheme for BSDE’s, The Annals of Applied Probability, Volume 14(1) (2004), pp. 459-488 | DOI | Zbl
Cité par Sources :