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A probability-free and continuous-time explanation of the equity premium and CAPM

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  • Vladimir Vovk
  • Glenn Shafer

Abstract

This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain a simple expression for the equity premium and derive a version of the capital asset pricing model.

Suggested Citation

  • Vladimir Vovk & Glenn Shafer, 2016. "A probability-free and continuous-time explanation of the equity premium and CAPM," Papers 1607.00830, arXiv.org.
    • Handle: RePEc:arx:papers:1607.00830
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    File URL: http://arxiv.org/pdf/1607.00830
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    References listed on IDEAS

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    1. Vladimir Vovk, 2011. "The Capital Asset Pricing Model as a corollary of the Black-Scholes model," Papers 1109.5144, arXiv.org.
    2. Vladimir Vovk, 2016. "Getting rich quick with the Axiom of Choice," Papers 1604.00596, arXiv.org, revised Mar 2017.
    3. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    4. Vladimir Vovk, 2011. "A simplified Capital Asset Pricing Model," Papers 1111.2846, arXiv.org.
    5. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    6. Malkiel, Burton G, 1995. "Returns from Investing in Equity Mutual Funds 1971 to 1991," Journal of Finance, American Finance Association, vol. 50(2), pages 549-572, June.
    7. Vladimir Vovk, 2015. "Purely pathwise probability-free Ito integral," Papers 1512.01698, arXiv.org, revised Jun 2016.
    8. Vladimir Vovk, 2009. "Continuous-time trading and the emergence of probability," Papers 0904.4364, arXiv.org, revised May 2015.
    9. Vladimir Vovk, 2011. "The efficient index hypothesis and its implications in the BSM model," Papers 1109.2327, arXiv.org.
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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, 2018. "Game-Theoretic Capital Asset Pricing in Continuous Time," Papers 1802.01556, arXiv.org.
    3. Vladimir Vovk, 2017. "Non-stochastic portfolio theory," Papers 1712.09108, arXiv.org, revised Feb 2018.

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