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

José Infante Acevedo and Tony Lelièvre

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 143, issue C, 14-34

Abstract: We study an algorithm which has been proposed by A. Ammar, B. Mokdad, F. Chinesta, R. Keunings in 2006 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 algorithms, as introduced by V.N. 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.

Keywords: Greedy algorithms; Black–Scholes partial differential equation; Variance reduction (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475416301240
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:143:y:2018:i:c:p:14-34

DOI: 10.1016/j.matcom.2016.07.013

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().