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Numerical approximation of BSDEs using local polynomial drivers and branching processes

Bouchard, Bruno; Tan, Xiaolu; Warin, Xavier; Zou, Yiyi (2017), Numerical approximation of BSDEs using local polynomial drivers and branching processes, Monte Carlo Methods and Applications. 10.1515/mcma-2017-0116

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Type
Article accepté pour publication ou publié
Date
2017
Nom de la revue
Monte Carlo Methods and Applications
Éditeur
De Gruyter
Identifiant publication
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Auteur(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Warin, Xavier

Zou, Yiyi
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the Picard iteration can be solved by using a representation in terms of branching diffusion systems , thus avoiding the need for a fine time discretization. In contrast to the previous literature on the numerical resolution of BSDEs based on branching processes, we prove the convergence of our numerical scheme without limitation on the time horizon. Numerical simulations are provided to illustrate the performance of the algorithm.
Mots-clés
BSDE; Monte Carlo methods; branching process