Comptes Rendus
no. 3-4
Probability Theory/Numerical Analysis
Reducing variance in the numerical solution of BSDEs
[Réduction de variance pour la solution numérique des BSDEs]

Présenté par : the Editorial Board

Samu Alanko1 ; Marco Avellaneda1, 2
1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
2 Finance Concepts SARL, 49-51, avenue Victor-Hugo, 75116 Paris, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 135-138.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.010
Samu Alanko 1 ; Marco Avellaneda 1, 2

1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
2 Finance Concepts SARL, 49-51, avenue Victor-Hugo, 75116 Paris, France 
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Samu Alanko; Marco Avellaneda. Reducing variance in the numerical solution of BSDEs. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 135-138. doi : 10.1016/j.crma.2013.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.010/

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