Probability Theory/Numerical Analysis
Reducing variance in the numerical solution of BSDEs
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 135-138.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.02.010
Alanko, Samu 1; Avellaneda, Marco 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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Alanko, Samu; Avellaneda, Marco. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.02.010/

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