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Getting rich quick with the Axiom of Choice

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  • Vladimir Vovk

Abstract

This paper proposes new get-rich-quick schemes that involve trading in a financial security with a non-degenerate price path. For simplicity the interest rate is assumed zero. If the price path is assumed continuous, the trader can become infinitely rich immediately after it becomes non-constant (if it ever does). If it is assumed positive, he can become infinitely rich immediately after reaching a point in time such that the variation of the log price is infinite in any right neighbourhood of that point (whereas reaching a point in time such that the variation of the log price is infinite in any left neighbourhood of that point is not sufficient). The practical value of these schemes is tempered by their use of the Axiom of Choice.

Suggested Citation

  • Vladimir Vovk, 2016. "Getting rich quick with the Axiom of Choice," Papers 1604.00596, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1604.00596
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    References listed on IDEAS

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    1. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    2. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    3. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
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    Cited by:

    1. Vladimir Vovk & Glenn Shafer, 2017. "Towards a probability-free theory of continuous martingales," Papers 1703.08715, arXiv.org.
    2. Vladimir Vovk & Glenn Shafer, 2016. "A probability-free and continuous-time explanation of the equity premium and CAPM," Papers 1607.00830, arXiv.org.

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