Efficient Algorithms for Universal Portfolios

Adam Kalai, Santosh Vempala; 3(Nov):423-440, 2002.


A constant rebalanced portfolio is an investment strategy that keeps the same distribution of wealth among a set of stocks from day to day. There has been much work on Cover's Universal algorithm, which is competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991, Helmbold et al, 1998, Blum and Kalai, 1999, Foster and Vohra, 1999, Vovk, 1998, Cover and Ordentlich, 1996a, Cover, 1996c). While this algorithm has good performance guarantees, all known implementations are exponential in the number of stocks, restricting the number of stocks used in experiments (Helmbold et al, 1998, Cover and Ordentlich, 1996a, Ordentlich and Cover, 1996b, Cover, 1996c, Blum and Kalai, 1999). We present an efficient implementation of the Universal algorithm that is based on non-uniform random walks that are rapidly mixing (Applegate and Kannan, 1991, Lovasz and Simonovits, 1992, Frieze and Kannan, 1999). This same implementation also works for non-financial applications of the Universal algorithm, such as data compression (Cover, 1996c) and language modeling (Chen et al, 1999).

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