https://enpc.hal.science/hal-00861892v1Infante Acevedo, José ArturoJosé ArturoInfante 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 ParisTechMICMAC - Methods and engineering of multiscale computing from atom to continuum - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTechA non linear approximation method for solving high dimensional partial differential equations: Application in Finance.HAL CCSD2013Greedy algorithmsBlack-Scholes partial differential equation[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Infante Acevedo, José Arturo2013-09-13 18:17:562022-01-11 11:16:202013-09-15 07:53:08enPreprints, Working Papers, ...https://enpc.hal.science/hal-00861892v1/documenthttps://enpc.hal.science/hal-00861892v1application/pdf1We 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.