IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v143y2018icp14-34.html
   My bibliography  Save this article

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

Author

Listed:
  • Infante Acevedo, José
  • Lelièvre, Tony

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.

Suggested Citation

  • Infante Acevedo, José & Lelièvre, Tony, 2018. "A non linear approximation method for solving high dimensional partial differential equations: Application in finance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 14-34.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:14-34
    DOI: 10.1016/j.matcom.2016.07.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475416301240
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2016.07.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:14-34. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.