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The role of measurability in game-theoretic probability

Author

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  • Vladimir Vovk

    (Royal Holloway, University of London)

Abstract

This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit.

Suggested Citation

  • Vladimir Vovk, 2017. "The role of measurability in game-theoretic probability," Finance and Stochastics, Springer, vol. 21(3), pages 719-739, July.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0336-4
    DOI: 10.1007/s00780-017-0336-4
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    References listed on IDEAS

    as
    1. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    2. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    3. Vladimir Vovk, 2010. "Rough paths in idealized financial markets," Papers 1005.0279, arXiv.org, revised Nov 2016.
    4. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
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    Citations

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    Cited by:

    1. Vidmar, Matija, 2021. "A nonclassical solution to a classical SDE and a converse to Kolmogorov’s zero–one law," Statistics & Probability Letters, Elsevier, vol. 175(C).
    2. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.

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    More about this item

    Keywords

    Axiom of choice; Continuous time; Game-theoretic probability; Incomplete markets; Measurability;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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