Universal portfolios with side information

Author

Cover, Thomas M. ; Ordentlich, Erik

Author_Institution

Dept. of Stat., Stanford Univ., CA, USA

Volume

42

Issue

2

fYear

1996

fDate

3/1/1996 12:00:00 AM

Firstpage

348

Lastpage

363

Abstract

We present a sequential investment algorithm, the μ-weighted universal portfolio with side information, which achieves, to first order in the exponent, the same wealth as the best side-information dependent investment strategy (the best state-constant rebalanced portfolio) determined in hindsight from observed market and side-information outcomes. This is an individual sequence result which shows the difference between the exponential growth wealth of the best state-constant rebalanced portfolio and the universal portfolio with side information is uniformly less than (d/(2n))log (n+1)+(k/n)log 2 for every stock market and side-information sequence and for all time n. Here d=k(m-1) is the number of degrees of freedom in the state-constant rebalanced portfolio with k states of side information and m stocks. The proof of this result establishes a close connection between universal investment and universal data compression

Keywords

commerce; data compression; economics; information theory; investment; stock markets; μ-weighted universal portfolio; exponential growth wealth; sequential investment algorithm; side information; state-constant rebalanced portfolio; stock market sequence; universal data compression; universal investment; universal portfolios; Data compression; Information theory; Investments; Portfolios; Probability distribution; Statistical distributions; Stochastic processes; Stock markets; Terrorism;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.485708

Filename

485708