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

Author

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  • Kei Takeuchi
  • Masayuki Kumon
  • Akimichi Takemura

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.

Suggested Citation

  • Kei Takeuchi & Masayuki Kumon & Akimichi Takemura, 2008. "Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time," Papers 0802.4311, arXiv.org, revised Mar 2008.
    • Handle: RePEc:arx:papers:0802.4311
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    File URL: http://arxiv.org/pdf/0802.4311
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    References listed on IDEAS

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    1. 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.
    2. Vladimir Vovk, 2007. "Continuous-time trading and emergence of volatility," Papers 0712.1483, arXiv.org, revised Dec 2007.
    3. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
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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, Springer;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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