关键词: 在线学习；专家意见；在线投资组合；交易费用；累积收益

Abstract: The weak aggregating algorithm is an online learning algorithm that dynamically weights the average of expert advice. In recent years, machine learning and artificial intelligence have been used to study online portfolio. An important feature of online portfolio strategy is that it does not make any statistical assumptions about stock prices, constructs an investment strategy based on historical data, and ensures that its cumulative gains are almost as good as benchmark strategy. Under the perspective of online sequence decision of weak aggregating algorithm, an improved exponential gradient portfolio strategy is designed, which is made up for the defeat that exponential gradient online portfolio strategy can not be combined with transaction costs. Firstly, according to the update method of exponential gradient online portfolio strategy, the expert advice pool representing the investment strategy is constructed, and on this basis, the weak aggregating algorithm is used to obtain the improved exponential gradient online portfolio strategy, which has proved to be competitive. Secondly, transaction costs are introduced into the improved exponential gradient online portfolio strategy, and the improved exponential gradient online portfolio strategy with transaction costs is further proposed. Significantly, it is theoretically proved that there is an asymptotical lower bound on the difference between the average of cumulative gain of the strategy and the best expert advice, so as to improve the practicability of exponential gradient online portfolio strategy effectively. Finally, an empirical analysis on historical stock data is utilized to test the performance of improved exponential gradient strategy. On these data, anexperimentisprovided to illustrate the feasibility as well as effectiveness of the strategy. Whether or not transaction costs are taken into account, the improved exponential gradient portfolio strategy performswell and achieves competitive performance in practical applications. Moreover, the empirical results showthatthe proposedstrategynotonlyperforms well in terms of returnbut also strikes a good balance betweenreturn and risk.

Key words: online learning; expert advice; online portfolio selection; transaction costs; cumulative gains