基于在线算法的改进指数梯度投资组合策略

Improved Exponential Gradient Portfolio Strategy Based on Online Algorithm

弱集成算法是对专家意见进行动态加权平均的在线学习算法。近年来,机器学习和人工智能等方法被用来研究在线投资组合问题。该文从弱集成算法的在线学习及其序列决策性角度出发,设计改进的指数梯度在线投资组合策略,以弥补指数梯度在线投资组合策略不能结合交易费用进行分析的缺陷。首先根据指数梯度在线投资组合策略的更新方法构建代表投资策略的专家意见池,并以此为基础应用弱集成算法加权集成专家意见得到改进的指数梯度在线投资组合策略,证明了该策略可与最优专家策略(基准策略)相媲美。其次将交易费用引入到改进的指数梯度在线投资组合策略中,进一步给出对应的投资策略,重要的是理论上证明了该策略实现的平均累积收益与最优专家策略实现的平均累积收益之间的差值存在渐进式下界,从而提高了指数梯度在线投资组合策略的实用性。最后利用国内外股票市场的历史数据进行实证分析,说明了改进的指数梯度在线投资组合策略的可行性和有效性。

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.