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Cover's universal portfolio, stochastic portfolio theory and the numeraire 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 as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result is model-free, i.e., not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory as initiated by R. Fernholz: the rebalancing rule need not to be constant anymore but may depend on the present state of the stock market. This model-free result is complemented by a comparison with the log-optimal numeraire portfolio when fixing a stochastic model of the stock market. Roughly speaking, under appropriate assumptions, the optimal long run yield coincides for the three approaches mentioned in the title of this paper. We present our results in discrete and continuous time.

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  • Christa Cuchiero & Walter Schachermayer & Ting-Kam Leonard Wong, 2016. "Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio," Papers 1611.09631, arXiv.org.
    • Handle: RePEc:arx:papers:1611.09631
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    References listed on IDEAS

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    Cited by:

    1. Constantinos Kardaras & Scott Robertson, 2018. "Ergodic robust maximization of asymptotic growth," Papers 1801.06425, arXiv.org.
    2. 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.

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