Cover's Universal Portfolio, Stochastic Portfolio Theory, and the Numéraire Portfolio

31 Pages Posted: 29 May 2020

See all articles by Christa Cuchiero

Christa Cuchiero

University of Vienna - Faculty of Science and Mathematics

Walter Schachermayer

University of Vienna

Ting‐Kam Leonard Wong

University of Toronto

Date Written: July 2019

Abstract

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.

Keywords: Diffusions on the unit simplex, ergodic Markov process, functionally generated portfolios, long‐only portfolios, log‐optimal portfolio, stochastic portfolio theory, universal portfolio

Suggested Citation

Cuchiero, Christa and Schachermayer, Walter and Wong, Ting‐Kam Leonard, Cover's Universal Portfolio, Stochastic Portfolio Theory, and the Numéraire Portfolio (July 2019). Mathematical Finance, Vol. 29, Issue 3, pp. 773-803, 2019, Available at SSRN: https://ssrn.com/abstract=3613891 or http://dx.doi.org/10.1111/mafi.12201

Christa Cuchiero (Contact Author)

University of Vienna - Faculty of Science and Mathematics ( email )

Vienna
Austria

Walter Schachermayer

University of Vienna

Bruenner Strasse 72
Vienna, 1090
Austria

Ting‐Kam Leonard Wong

University of Toronto

Toronto, M5S 3G8
Canada

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
0
Abstract Views
270
PlumX Metrics