Based on the momentum principle and adaptive learning mechanism, we design online portfolio selection strategies, which are suitable for nonstationary financial market. Firstly, we propose a Moving-window-based Adaptive Exponential Gradient (MAEG) strategy, which updates the learning rate of the EG algorithm by maximizing the recent cumulative return using the price data in a fixed length moving window. Secondly, we consider a special case where all-historical price data is used to design another strategy named Adaptive Exponential Gradient (AEG). Finally, we conduct an extensive numerical analysis using real price data and the empirical results show that the performance of the proposed strategies is steadily superior to some online strategies. In addition, MAEG and AEG are able to withstand certain transaction costs, which further supports their practical applicability in trading applications.

Based on the momentum principle and adaptive learning mechanism, we design online portfolio selection strategies, which are suitable for nonstationary financial market. Firstly, we propose a Moving-window-based Adaptive Exponential Gradient (MAEG) strategy, which updates the learning rate of the EG algorithm by maximizing the recent cumulative return using the price data in a fixed length moving window. Secondly, we consider a special case where all-historical price data is used to design another strategy named Adaptive Exponential Gradient(AEG)。最后，我们使用真实价格数据进行了广泛的数值分析，实证结果表明，所提出的策略的性能稳定地优于一些在线策略。此外，MAEG 和 AEG 能够承受一定的交易成本，这进一步支持了它们在交易应用中的实际适用性。