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Continuous-time trading and emergence of randomness

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  • Vladimir Vovk

Abstract

A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on "qualitative" results, stated in terms of order (or order topology) rather than in terms of the precise values taken by the price processes (assumed continuous).

Suggested Citation

  • Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
    • Handle: RePEc:arx:papers:0712.1275
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    File URL: http://arxiv.org/pdf/0712.1275
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    References listed on IDEAS

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    1. Kei Takeuchi & Masayuki Kumon & Akimichi Takemura, 2007. "A new formulation of asset trading games in continuous time with essential forcing of variation exponent," Papers 0708.0275, arXiv.org, revised Jan 2010.
    2. Yasunori Horikoshi & Akimichi Takemura, 2007. "Implications of contrarian and one-sided strategies for the fair-coin game," Papers math/0703743, arXiv.org.
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    Cited by:

    1. Vladimir Vovk, 2007. "Continuous-time trading and emergence of volatility," Papers 0712.1483, arXiv.org, revised Dec 2007.
    2. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    3. 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.

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    1. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    2. Vladimir Vovk, 2007. "Continuous-time trading and emergence of volatility," Papers 0712.1483, arXiv.org, revised Dec 2007.
    3. Kei Takeuchi & Masayuki Kumon & Akimichi Takemura, 2007. "A new formulation of asset trading games in continuous time with essential forcing of variation exponent," Papers 0708.0275, arXiv.org, revised Jan 2010.

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