IDEAS home Printed from https://ideas.repec.org/p/cfi/fseres/cf547.html
   My bibliography  Save this paper

Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with nonlinear coefficients

Author

Listed:
  • Akihiko Takahashi

    (University of Tokyo)

  • Toshihiro Yamada

    (Hitotsubashi University, Japan Science and Technology Agency (JST))

Abstract

This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion method with a deep learning-based algorithm. In particular, the mathematical justification on the spatial approximation is provided, and a numerical example for a 100 dimensional Kolmogorov PDE shows effectiveness of our method.

Suggested Citation

  • Akihiko Takahashi & Toshihiro Yamada, 2022. "Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with nonlinear coefficients," CARF F-Series CARF-F-547, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf547
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:cfi:fseres:cf547. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/catokjp.html .

    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.