IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i03ns0219024914500186.html
   My bibliography  Save this article

Utility Theory Front To Back — Inferring Utility From Agents' Choices

Author

Listed:
  • ALEXANDER M. G. COX

    (Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom)

  • DAVID HOBSON

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom)

  • JAN OBłÓJ

    (Mathematical Institute and Oxford–Man Institute of Quantitative Finance, University of Oxford, Oxford OX1 3LB, United Kingdom)

Abstract

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.

Suggested Citation

  • Alexander M. G. Cox & David Hobson & Jan Obłój, 2014. "Utility Theory Front To Back — Inferring Utility From Agents' Choices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 1-44.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:03:n:s0219024914500186
    DOI: 10.1142/S0219024914500186
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500186
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500186?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    2. Haoyang Cao & Zhengqi Wu & Renyuan Xu, 2024. "Inference of Utilities and Time Preference in Sequential Decision-Making," Papers 2405.15975, arXiv.org, revised Jun 2024.

    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:wsi:ijtafx:v:17:y:2014:i:03:n:s0219024914500186. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.