Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression

Abstract : We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration by parts-representation of the Z-component by [Ma-Zhang 2002]. When the sequence of conditional expectations is computed using empirical least-squares regressions, we establish, under general conditions, tight error bounds as the time-average of local regression errors only (up to logarithmic factors). We compute the algorithm complexity by a suitable optimization of the parameters, depending on the dimension and the smoothness of value functions, in the limit as the number of grid times goes to infinity. The estimates take into account the regularity of the terminal function.
Type de document :
Pré-publication, Document de travail
2014
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00855760
Contributeur : Emmanuel Gobet <>
Soumis le : mardi 25 mars 2014 - 16:10:28
Dernière modification le : jeudi 9 février 2017 - 15:15:55

Fichier

MalWeightsRev-Hal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00855760, version 2

Collections

Citation

Emmanuel Gobet, Plamen Turkedjiev. Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression. 2014. 〈hal-00855760v2〉

Partager

Métriques

Consultations de la notice

506

Téléchargements de fichiers

351