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Continuous-time trading and emergence of volatility

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  • Vladimir Vovk
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    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.

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    File URL: http://arxiv.org/pdf/0712.1483
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0712.1483.

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    Date of creation: Dec 2007
    Date of revision: Dec 2007
    Publication status: Published in Electronic Communications in Probability 13, 319 - 324 (2008)
    Handle: RePEc:arx:papers:0712.1483

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    Web page: http://arxiv.org/

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    1. 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. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised Aug 2010.
    2. 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.
    3. Vladimir Vovk, 2010. "Rough paths in idealized financial markets," Papers 1005.0279, arXiv.org, revised May 2011.

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