# ROBUST INVESTMENT.

## Abstract

Summary form only given. Let stock prices be represented by a discrete, positive sequence of vectors, where the proportionate change in price of a given stock during a given investment period is chosen from a finite set of possible values. No distribution on stock prices is assumed. A sequential portfolio strategy is exhibited that epsilon -achieves the rate of growth of capital attained by the log-optimal portfolio based on prior knowledge of the n-period empirical distribution. Moreover, for a horse race model, a betting strategy is exhibited that earns money at an exponential rate and earns within a polynomial factor as much money as the log-optimal portfolio based on prior knowledge of the n-period empirical distribution of winners and end-play. This result, which holds for every sample sequence, corresponds to universal noiseless coding. It suggests that a similar result holds for the more general stock market model. In addition, these investment strategies are much easier to compute than the Cover-Gluss strategy.