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.

中文翻译：

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Cover 的通用投资组合、随机投资组合理论和计价投资组合。

Cover 著名的定理指出，正确选择的“通用”投资组合的长期收益率几乎与回顾性选择的最佳恒定再平衡投资组合的长期收益率一样好。“普遍性”指的是这个结果是无模型的，也就是说，不依赖于潜在的随机过程。我们将 Cover 定理扩展到随机投资组合理论的设置：以市场投资组合为基准，再平衡规则不再是常数，而是可能取决于股票市场的当前状态。通过固定股票市场的随机模型，这个无模型的结果通过与 numéraire 投资组合的比较得到补充。粗略地说，在适当的假设下，本文标题中提到的三种方法的渐近增长率是一致的。我们以离散时间和连续时间呈现结果。