Journal Articles Mathematics and Computers in Simulation Year : 2018

A non linear approximation method for solving high dimensional partial differential equations: Application in finance

Abstract

We 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.
Fichier principal
Vignette du fichier
papier_greedy_bs.pdf (343) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00861892 , version 1 (13-09-2013)
hal-00861892 , version 2 (17-09-2013)

Identifiers

Cite

José Infante Acevedo, Tony Lelièvre. A non linear approximation method for solving high dimensional partial differential equations: Application in finance. Mathematics and Computers in Simulation, 2018, 143, pp.14-34. ⟨10.1016/j.matcom.2016.07.013⟩. ⟨hal-00861892v2⟩
385 View
546 Download

Altmetric

Share

More