IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1906.02216.html
   My bibliography  Save this paper

Game-Theoretic Optimal Portfolios in Continuous Time

Author

Listed:
  • Alex Garivaltis

Abstract

We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the `numerator player') picks $b$ so as to maximize $\mathbb{E}[V_t(b)/V_t(c)]$, while Player 2 (the `denominator player') picks $c$ so as to minimize it. In the unique Nash equilibrium, both players use the continuous-time Kelly rule $b^*=c^*=\Sigma^{-1}(\mu-r\textbf{1})$, where $\Sigma$ is the covariance of instantaneous returns per unit time, $\mu$ is the drift vector of the stock market, and $\textbf{1}$ is a vector of ones. Thus, even over very short intervals of time $[0,t]$, the desire to perform well relative to other traders leads one to adopt the Kelly rule, which is ordinarily derived by maximizing the asymptotic exponential growth rate of wealth. Hence, we find agreement with Bell and Cover's (1988) result in discrete time.

Suggested Citation

  • Alex Garivaltis, 2019. "Game-Theoretic Optimal Portfolios in Continuous Time," Papers 1906.02216, arXiv.org, revised Oct 2022.
  • Handle: RePEc:arx:papers:1906.02216
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1906.02216
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Alex Garivaltis, 2019. "Nash Bargaining Over Margin Loans to Kelly Gamblers," Risks, MDPI, vol. 7(3), pages 1-14, August.
    2. Alex Garivaltis, 2019. "Game-Theoretic Optimal Portfolios for Jump Diffusions," Games, MDPI, vol. 10(1), pages 1-9, February.
    3. Alex Garivaltis, 2019. "A Note on Universal Bilinear Portfolios," Papers 1907.09704, arXiv.org, revised Oct 2022.
    4. Alex Garivaltis, 2021. "A Note on Universal Bilinear Portfolios," IJFS, MDPI, vol. 9(1), pages 1-17, February.

    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:1906.02216. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.