Abstract:
Cover’s celebrated theorem states that the long run yield of a properly chosen “universal” constant rebalanced 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 modelfree, 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 result is complimented by a comparison with the log-optimal num ́eraire 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. We present our results in discrete as well as in continuous time.
The talk is based on joint work with Walter Schachermayer and Leonard Wong.