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

A new formulation of asset trading games in continuous time with essential forcing of variation exponent


Author Info

  • Kei Takeuchi
  • Masayuki Kumon
  • Akimichi Takemura
Registered author(s):


    We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can depend on the past path of the market. We prove that an investor can essentially force that the asset price path behaves with the variation exponent exactly equal to two. Our proof is based on embedding high-frequency discrete-time games into the continuous-time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi (Stoch. Anal. Appl. 26 (2008) 1161--1180) for discrete-time coin-tossing games. We also show that the main growth part of the investor's capital processes is clearly described by the information quantities, which are derived from the Kullback--Leibler information with respect to the empirical fluctuation of the asset price.

    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 0708.0275.

    as in new window
    Date of creation: Aug 2007
    Date of revision: Jan 2010
    Publication status: Published in Bernoulli 2009, Vol. 15, No. 4, 1243-1258
    Handle: RePEc:arx:papers:0708.0275

    Contact details of provider:
    Web page:

    Related research



    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. V. Vovk, 1993. "Forecasting point and continuous processes: Prequential analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 2(1), pages 189-217, December.
    2. Yasunori Horikoshi & Akimichi Takemura, 2007. "Implications of contrarian and one-sided strategies for the fair-coin game," Papers math/0703743,
    3. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
    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. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364,, revised Aug 2010.
    2. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275,, revised Dec 2007.


    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:0708.0275. 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.