Universal Portfolios Generated by the Bregman Divergence

The Bregman divergence of two probability vectors is a stronger form of the f-divergence introduced by Csiszar. Two versions of the Bregman universal portfolio are presented by exploiting the mean-value theorem. The explicit form of the Bregman universal portfolio generated by a function of a convex polynomial is derived and studied empirically. This portfolio can be regarded as another generalized of the well-known Helmbold portfolio. By running the portfolios on selected stock price data sets from the local stock exchange, it is shown that it is possible to increase the wealth of the investor by using the portfolios in investment.