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Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time

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  • Kei Takeuchi
  • Masayuki Kumon
  • Akimichi Takemura
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    Abstract

    We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trials. We then apply our scheme to asset trading games in continuous time and derive the exponential growth rate of the investor's capital when the variation exponent of the asset price path deviates from two.

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    File URL: http://arxiv.org/pdf/0802.4311
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0802.4311.

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    Date of creation: Feb 2008
    Date of revision: Mar 2008
    Publication status: Published in Stochastic Analysis and Applications, Vol.28 (2010), 842-861
    Handle: RePEc:arx:papers:0802.4311

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    Web page: http://arxiv.org/

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    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.:
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    1. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
    2. Vladimir Vovk, 2007. "Continuous-time trading and emergence of volatility," Papers 0712.1483, arXiv.org, revised Dec 2007.
    3. Masayuki Kumon & Akimichi Takemura & Kei Takeuchi, 2005. "Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games," Papers math/0510662, arXiv.org, revised Sep 2008.
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    Cited by:
    1. Kei Takeuchi & Akimichi Takemura & Masayuki Kumon, 2011. "New Procedures for Testing Whether Stock Price Processes are Martingales," Computational Economics, Society for Computational Economics, vol. 37(1), pages 67-88, January.
    2. Kei Takeuchi & Akimichi Takemura & Masayuki Kumon, 2009. "New procedures for testing whether stock price processes are martingales," Papers 0907.3273, arXiv.org, revised Feb 2010.

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