2016/11/29 by Christa Cuchiero, Cuchiero, Christa, Walter Schachermayer +3 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1611.09631
openalex publication_date 2016/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.