IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1607.00830.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1607.00830
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vladimir Vovk & Glenn Shafer, 2017. "Towards a probability-free theory of continuous martingales," Papers 1703.08715, arXiv.org.
    2. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.
    3. Vladimir Vovk, 2016. "Another example of duality between game-theoretic and measure-theoretic probability," Papers 1608.02706, arXiv.org.
    4. Vladimir Vovk, 2017. "The role of measurability in game-theoretic probability," Finance and Stochastics, Springer, vol. 21(3), pages 719-739, July.
    5. Vladimir Vovk, 2016. "Getting rich quick with the Axiom of Choice," Papers 1604.00596, arXiv.org, revised Mar 2017.
    6. Vladimir Vovk, 2015. "Purely pathwise probability-free Ito integral," Papers 1512.01698, arXiv.org, revised Jun 2016.
    7. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    8. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    9. Lesiba Ch. Galane & Rafa{l} M. {L}ochowski & Farai J. Mhlanga, 2017. "On the quadratic variation of the model-free price paths with jumps," Papers 1710.07894, arXiv.org, revised May 2018.
    10. Christian Bender & Sebastian Ferrando & Alfredo Gonzalez, 2021. "Model-Free Finance and Non-Lattice Integration," Papers 2105.10623, arXiv.org.
    11. Andrew L. Allan & Chong Liu & David J. Promel, 2021. "A C\`adl\`ag Rough Path Foundation for Robust Finance," Papers 2109.04225, arXiv.org, revised May 2023.
    12. Daniel Bartl & Michael Kupper & David J. Promel & Ludovic Tangpi, 2017. "Duality for pathwise superhedging in continuous time," Papers 1705.02933, arXiv.org, revised Apr 2019.
    13. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    14. Mathias Beiglböck & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Prömel, 2017. "Pathwise superreplication via Vovk’s outer measure," Finance and Stochastics, Springer, vol. 21(4), pages 1141-1166, October.
    15. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    16. Rafa{l} M. {L}ochowski, 2015. "Integration with respect to model-free price paths with jumps," Papers 1511.08194, arXiv.org, revised Sep 2016.
    17. Łochowski, Rafał M. & Perkowski, Nicolas & Prömel, David J., 2018. "A superhedging approach to stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4078-4103.
    18. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    19. Lesiba Ch. Galane & Rafa{l} M. {L}ochowski & Farai J. Mhlanga, 2018. "On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales," Papers 1807.05692, arXiv.org, revised Feb 2022.
    20. Christiane Goodfellow & Dirk Schiereck & Steffen Wippler, 2013. "Are behavioural finance equity funds a superior investment? A note on fund performance and market efficiency," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 111-119, April.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1607.00830. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.