IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v46y2021i4p1250-1281.html
   My bibliography  Save this article

A Mean Field Game of Optimal Portfolio Liquidation

Author

Listed:
  • Guanxing Fu

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Paulwin Graewe

    (Deloitte Consulting GmbH, 10719 Berlin, Germany)

  • Ulrich Horst

    (Department of Mathematics and School of Business and Economics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany)

  • Alexandre Popier

    (Laboratoire Manceau de Mathématiques, Le Mans Université, 72058 Le Mans Cedex 9, France)

Abstract

We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with a finite terminal value yet a singular driver. Extending the method of continuation to linear-quadratic FBSDEs with a singular driver, we prove that the MFG has a unique solution. Our existence and uniqueness result allows proving that the MFG with a possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.

Suggested Citation

  • Guanxing Fu & Paulwin Graewe & Ulrich Horst & Alexandre Popier, 2021. "A Mean Field Game of Optimal Portfolio Liquidation," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1250-1281, November.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:4:p:1250-1281
    DOI: 10.1287/moor.2020.1094
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2020.1094
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2020.1094?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
    ---><---

    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:inm:ormoor:v:46:y:2021:i:4:p:1250-1281. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.