MIT Department of Electrical Engineering & Computer Science

Universal Data Compression and Universal Portfolios

Thomas M. Cover
Stanford University

Thursday, March 2, 2000
4:00 PM (reception following)
Room 35-225
LIDS Colloquium

Abstract

The theory of universal data compression and universal investment shows striking similarities. In data compression , the cost (in bits) of universality is the radius of the minimum information ball that contains all the source distributions. Similarly, in universal investment, the cost of universality (in growth rate of wealth) is the radius of the minimum relative growth rate ball containing all the market distributions. Both these costs can be shown to be asymptotically negligible. As a consequence, there exists a universal portfolio that has the same asymptotic growth rate of wealth as the best constant rebalanced portfolio given perfect hindsight.

We also note close parallels when side information is considered. In general. the increase in growth rate due to side information is upper bounded by the mutual information between the market and the side information. We will investigate the value of side information for the universal portfolio. In joint work with E. Ordentlich and D. Julian we let the side information be the moving average of the past price relatives, yielding striking gains in performance.

A short reception will follow in the LIDS Reading Room (35-338) ------------------------------------------------------------------------------ Biography:

Professor Thomas M. Cover received the B.S. degree in physics from MIT in 1960 and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, in 1961 and 1964, respectively. He is currently a Professor in the Departments of Electrical Engineering and Statistics at Stanford University, where he teaches and does research in the areas of machine learning, communication and information theory, and pattern recognition. Dr. Cover is past President of IEEE Information Theory Society and the Shannon Award Winner in 1990. He received the Richard W. Hamming Medal from the IEEE in 1997. He is a member of the Institute of Mathematical Statistics, the American Mathematical Society, the New York Academy of Sciences, and Sigma Xi.