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

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 constant rebalanced portfolio. The "universality" refers to the fact that this result is , 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.