[Réduction de variance pour la solution numérique des BSDEs]
Les méthodes numériques basées sur la discrétisation de pas de temps et lʼestimation dʼespérances conditionnelles pour la résolution dʼéquations différentielles stochastiques rétrogrades (BSDEs) ont fait lʼobjet dʼétudes récentes, en particulier pour leurs applications dans le domaine de la finance. Nous proposons ici une technique basée sur les variables de contrôle permettant de réduire lʼerreur dans la simulation des estimateurs dʼespérance conditionnelle. Ces modifications peuvent être adaptées facilement aux algorithmes connus pour augmenter leur efficacité, avec sensiblement le même temps de calcul.
Numerical methods based on time discretization and estimation of conditional expectations for solving backward stochastic differential equations (BSDEs) have been the object of considerable research, particularly in view of the applications to finance. We introduce and implement a simple control variate technique to reduce the simulation error of the conditional expectation estimates in BSDE methods. These modifications increase the accuracy of the existing algorithms without additional computational cost.
Accepté le :
Publié le :
@article{CRMATH_2013__351_3-4_135_0,
author = {Alanko, Samu and Avellaneda, Marco},
title = {Reducing variance in the numerical solution of {BSDEs}},
journal = {Comptes Rendus. Math\'ematique},
pages = {135--138},
publisher = {Elsevier},
volume = {351},
number = {3-4},
year = {2013},
doi = {10.1016/j.crma.2013.02.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.02.010/}
}
TY - JOUR AU - Alanko, Samu AU - Avellaneda, Marco TI - Reducing variance in the numerical solution of BSDEs JO - Comptes Rendus. Mathématique PY - 2013 SP - 135 EP - 138 VL - 351 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.02.010/ DO - 10.1016/j.crma.2013.02.010 LA - en ID - CRMATH_2013__351_3-4_135_0 ER -
%0 Journal Article %A Alanko, Samu %A Avellaneda, Marco %T Reducing variance in the numerical solution of BSDEs %J Comptes Rendus. Mathématique %D 2013 %P 135-138 %V 351 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.02.010/ %R 10.1016/j.crma.2013.02.010 %G en %F CRMATH_2013__351_3-4_135_0
Alanko, Samu; Avellaneda, Marco. Reducing variance in the numerical solution of BSDEs. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 135-138. doi : 10.1016/j.crma.2013.02.010. http://www.numdam.org/articles/10.1016/j.crma.2013.02.010/
[1] Pricing and hedging derivative securities in markets with uncertain volatilities, Appl. Math. Finance, Volume 2 (1995), pp. 73-88
[2] Discrete-time approximation and Monte Carlo simulation of backward stochastic differential equations, Stochastic Process. Appl., Volume 111 (2004), pp. 175-206
[3] Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs, Comm. Pure Appl. Math., Volume 60 (2006), pp. 1081-1110
[4] A probabilistic numerical method for fully nonlinear parabolic PDEs, Ann. Appl. Probab., Volume 21 (2011), pp. 1322-1364
[5] Solving BSDE with adaptive control variate, SIAM J. Numer. Anal., Volume 48 (2010), pp. 257-277
[6] A regression-based Monte Carlo method to solve backward stochastic differential equations, Ann. Appl. Probab., Volume 15 (2005), pp. 2172-2202
[7] Uncertain volatility model: A Monte-Carlo approach, J. Comput. Finance, Volume 14 (2011), pp. 37-71
[8] A numerical scheme for BSDEs, Ann. Appl. Probab., Volume 14 (2004), pp. 459-488
Cité par Sources :
