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Continuous-time trading and emergence of randomness

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  • Vladimir Vovk
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    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).

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    File URL: http://arxiv.org/pdf/0712.1275
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0712.1275.

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    Date of creation: Dec 2007
    Date of revision: Dec 2007
    Publication status: Published in Stochastics 81, 455 - 466 (2009)
    Handle: RePEc:arx:papers:0712.1275

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    Web page: http://arxiv.org/

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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.
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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 Aug 2010.
    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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