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Continuous-time trading and emergence of volatility

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  • Vladimir Vovk

Abstract

This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.

Suggested Citation

  • Vladimir Vovk, 2007. "Continuous-time trading and emergence of volatility," Papers 0712.1483, arXiv.org, revised Dec 2007.
    • Handle: RePEc:arx:papers:0712.1483
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    File URL: http://arxiv.org/pdf/0712.1483
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    References listed on IDEAS

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    1. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
    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, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    2. Vladimir Vovk, 2010. "Rough paths in idealized financial markets," Papers 1005.0279, arXiv.org, revised Nov 2016.
    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. 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.
    2. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    3. Vladimir Vovk, 2007. "Continuous-time trading and emergence of randomness," Papers 0712.1275, arXiv.org, revised Dec 2007.
    4. 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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