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://archive.numdam.org/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://archive.numdam.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 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://archive.numdam.org/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://archive.numdam.org/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 | MR | Zbl
[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 | MR | Zbl
[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 | MR | Zbl
[5] Numerical methods for backward stochastic differential equations, Numerical methods in finance, Cambridge University Press, 1997, pp. 232-244 | MR | Zbl
[6] Backward stochastic differential equations with reflection and Dynkin games, The Annals of Probability, Volume 24 (1996), pp. 2024-2056 | DOI | MR | Zbl
[7] Numerical methods for forward-backward stochastic differential equations, Annals of Applied Probability, Volume 6 (1996), pp. 940-968 | DOI | MR | Zbl
[8] Backward stochastic differential equations in finance, Mathematical Finance (1997), pp. 1-71 | DOI | MR | Zbl
[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 | MR | Zbl
[11] Zero-sum stochastic differential games and BSDEs, Systems and Control letters, Volume 24 (1995), pp. 259-263 | DOI | MR | Zbl
[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 | MR | Zbl
[14] Representation theorems for backward stochastic differential equations, The Annals of Applied Probability, Volume 12(4) (2002), pp. 1390-1418 | MR | Zbl
[15] 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] 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
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