IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v33y2023i4p1370-1411.html
   My bibliography  Save this article

Epstein‐Zin utility maximization on a random horizon

Author

Listed:
  • Joshua Aurand
  • Yu‐Jui Huang

Abstract

This paper solves the consumption‐investment problem under Epstein‐Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed‐horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.

Suggested Citation

  • Joshua Aurand & Yu‐Jui Huang, 2023. "Epstein‐Zin utility maximization on a random horizon," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1370-1411, October.
  • Handle: RePEc:bla:mathfi:v:33:y:2023:i:4:p:1370-1411
    DOI: 10.1111/mafi.12404
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12404
    Download Restriction: no

    File URL: https://libkey.io/10.1111/mafi.12404?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
    ---><---

    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:bla:mathfi:v:33:y:2023:i:4:p:1370-1411. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.