https://hal-enpc.archives-ouvertes.fr/hal-00861892v2Infante Acevedo, JoséJoséInfante AcevedoCERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTechLelièvre, TonyTonyLelièvreCERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTechMATHERIALS - MATHematics for MatERIALS - CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech - Inria de Paris - Inria - Institut National de Recherche en Informatique et en AutomatiqueA non linear approximation method for solving high dimensional partial differential equations: Application in financeHAL CCSD2018Variance reductionBlack-Scholes partial differential equationGreedy algorithms[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Infante Acevedo, José Arturo2013-09-17 07:39:262022-07-08 10:09:282013-09-17 08:17:35enJournal articleshttps://hal-enpc.archives-ouvertes.fr/hal-00861892v2/document10.1016/j.matcom.2016.07.013https://hal-enpc.archives-ouvertes.fr/hal-00861892v1application/pdf2We study an algorithm which has been proposed by Chinesta et al. to solve high-dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum. This algorithm is related to the so-called greedy algorithm introduced by Temlyakov. In this paper, we investigate the application of the greedy algorithm in finance and more precisely to the option pricing problem. We approximate the solution to the Black-Scholes equation and we propose a variance reduction method. In numerical experiments, we obtain results for up to 10 underlyings. Besides, the proposed variance reduction method permits an important reduction of the variance in comparison with a classical Monte Carlo method.