Advanced Search
MyIDEAS: Login to save this paper or follow this series

Asymptotics of the probability minimizing a "down-side" risk


Author Info

  • Hiroaki Hata
  • Hideo Nagai
  • Shuenn-Jyi Sheu
Registered author(s):


    We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain explicit solutions for the primal problem.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by in its series Papers with number 1001.2131.

    as in new window
    Date of creation: Jan 2010
    Date of revision:
    Publication status: Published in Annals of Applied Probability 2010, Vol. 20, No. 1, 52-89
    Handle: RePEc:arx:papers:1001.2131

    Contact details of provider:
    Web page:

    Related research


    This paper has been announced in the following NEP Reports:


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, Elsevier, vol. 116(1-2), pages 365-386.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:
    1. Hiroaki Hata, 2011. "“Down-Side Risk” Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates," Asia-Pacific Financial Markets, Springer, Springer, vol. 18(1), pages 69-87, March.
    2. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Papers 1408.6455,
    3. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Working Papers, HAL hal-01058657, HAL.
    4. Ichihara, Naoyuki, 2012. "Large time asymptotic problems for optimal stochastic control with superlinear cost," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 122(4), pages 1248-1275.
    5. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer, Springer, vol. 18(4), pages 385-403, November.
    6. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(3), pages 1046-1082.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1001.2131. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.

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