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Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio

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  • Christa Cuchiero
  • Walter Schachermayer
  • Ting‐Kam Leonard Wong

Abstract

Cover's celebrated theorem states that the long‐run yield of a properly chosen “universal” portfolio is almost as good as that of the best retrospectively chosen constant rebalanced portfolio. The “universality” refers to the fact that this result is model‐free, that is, not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory: the market portfolio is taken as the numéraire, and the rebalancing rule need not be constant anymore but may depend on the current state of the stock market. By fixing a stochastic model of the stock market this model‐free result is complemented by a comparison with the numéraire portfolio. Roughly speaking, under appropriate assumptions the asymptotic growth rate coincides for the three approaches mentioned in the title of this paper. We present results in both discrete and continuous time.

Suggested Citation

  • Christa Cuchiero & Walter Schachermayer & Ting‐Kam Leonard Wong, 2019. "Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 773-803, July.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:3:p:773-803
    DOI: 10.1111/mafi.12201
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    References listed on IDEAS

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    Cited by:

    1. Peter Baxendale & Ting-Kam Leonard Wong, 2019. "Random concave functions," Papers 1910.13668, arXiv.org, revised May 2021.
    2. Donghan Kim, 2019. "Open Markets," Papers 1912.13110, arXiv.org.
    3. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.
    4. Ioannis Karatzas & Donghan Kim, 2021. "Open markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1111-1161, October.

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