In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
Mots clés : backward stochastic differential equations, reflected stochastic differential equations with one barrier, numerical algorithm, numerical simulation
@article{M2AN_2011__45_2_335_0,
author = {Peng, Shige and Xu, Mingyu},
title = {Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: {Convergence} and simulations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {335--360},
publisher = {EDP-Sciences},
volume = {45},
number = {2},
year = {2011},
doi = {10.1051/m2an/2010059},
mrnumber = {2804642},
zbl = {1269.65008},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010059/}
}
TY - JOUR AU - Peng, Shige AU - Xu, Mingyu TI - Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 335 EP - 360 VL - 45 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010059/ DO - 10.1051/m2an/2010059 LA - en ID - M2AN_2011__45_2_335_0 ER -
%0 Journal Article %A Peng, Shige %A Xu, Mingyu %T Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 335-360 %V 45 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010059/ %R 10.1051/m2an/2010059 %G en %F M2AN_2011__45_2_335_0
Peng, Shige; Xu, Mingyu. Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 335-360. doi : 10.1051/m2an/2010059. http://www.numdam.org/articles/10.1051/m2an/2010059/
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