A class of on-line portfolio selection algorithms based on linear learning

On-line portfolio is a sequential investment algorithm during a long period and makes portfolio decision without any statistical assumption about the behavior of the market. A constant rebalanced portfolio (CRP) is an investment strategy which adopts the same portfolio vector on each trading period. Design of on-line portfolio algorithms which are competitive with the best constant rebalanced portfolio (BCRP) is a hot topic recently. In this paper, we present a new on-line portfolio selection strategy, which computes the new portfolio vector based completely on on-line learning of linear functions. The proposed algorithm is useful since it gives the investor a whole range of choices for the on-line portfolios. Using the technique of taking relative entropy as a distance function, we prove that the new algorithm is a universal portfolio, which exhibits the same asymptotic growth rate in normalized natural logarithmic wealth as the BCRP for any sequence of price relatives. Experiments on several New York Stock Exchange dates also show the good performance of the new strategy.