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Non-stochastic portfolio theory

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  • Vladimir Vovk

Abstract

This paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio theory and discusses connections with Stroock-Varadhan martingales.

Suggested Citation

  • Vladimir Vovk, 2017. "Non-stochastic portfolio theory," Papers 1712.09108, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1712.09108
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    References listed on IDEAS

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    1. Vladimir Vovk & Glenn Shafer, 2016. "A probability-free and continuous-time explanation of the equity premium and CAPM," Papers 1607.00830, arXiv.org.
    2. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    3. Fernholz, Robert, 1999. "On the diversity of equity markets," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 393-417, April.
    4. Dawid, A. Philip & de Rooij, Steven & Shafer, Glenn & Shen, Alexander & Vereshchagin, Nikolai & Vovk, Vladimir, 2011. "Insuring against loss of evidence in game-theoretic probability," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 157-162, January.
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