Universal Portfolio using the Best Current-Run Parameter

Abstract

The mixture-current-run universal portfolio introduced by Tan and Lim can extract the best daily wealth when it is implemented on different types of universal portfolios like the Helmbold and chi-square divergence universal portfolios. In this paper, we demonstrate another application of the mixture-current-run universal portfolio in extracting the best daily wealth due to the best parameter from the same parametric family of universal portfolios. The range of the parameter is discretized and the mixturecurrent-run universal portfolio is implemented on the different universal portfolios corresponding to the discretized parameters. Empirically, we demonstrate the performance of the portfolio by running it on some selected stock-data sets from the local stock exchange. The problem of selecting the best parameter at the outset is avoided by using the best current-run parameter in daily trading of the market and at the same time the best daily wealth is added to the accumulated wealth. Keywords: Investment Wealth; Mixture-Current-Run Universal Portfolio; Best Parameter. 2010 Mathematics Subject Classification: 91B28; 62P05