Research On Competitive Online Portfolio Selection Strategy By Aggregating Expert Advices

The literatures on classical portfolio problems often make assumptions about stock prices.However,the fluctuation of stock prices in the securities market is unstable.Thus,it is difficult to characterize the fluctuation of securities prices with a suitable stochastic process,which limits the application of the classical mean-variance model.The Weak Aggregating Algorithm,one of the online learning algorithms,can make decisions depending only on historical information rather than the information from statistical assumptions.It constructs online strategies by learning from different expert advices and aggregating them;and the online strategy can track the best expert advices.such an algorithm is helpful for the online decision makers to effectively integrate various types of information and make decisions.The online portfolio problem is a sequence decision problem,which makes dynamic asset allocations only based on historical data.Hence,the Weak Aggregating Algorithm can be used to study online portfolio problems.This paper considers that transaction cost is an important factor on investment decisions.On the basis of making no statistical assumptions about the future price and trend of stocks,the Weak Aggregating Algorithm is applied to design online portfolio selection strategies with transaction costs by integrating static expert advices and dynamic expert advices,respectively.Static expert advices refer to any Constant Rebalanced Portfolio strategies regarded as experts.And the static expert advices remain the same at all investment stages.Dynamic expert advices refer to the recommended portfolios updated by learning the optimal portfolio strategy of the previous investment using an exponential smoothing method.It is necessary to analyze the competitive performance of the proposed strategies.Hence,from the perspectives of theory and numerical examples,this paper further verifies the competitive performance of the proposed online ordering strategies.In theory,it is proved proved that the cumulative gains of online portfolio strategies is as much as that of the best expert,which means that the proposed strategies have good competitive performance.In terms of numerical examples,based on the domestic and foreign stock market data,the analyses are conducted from the perspectives of returns,risks,risk-adjusted returns,and transaction costs' sensitivity.The result shows that in case with transaction costs,the cumulative wealth achieved by the proposed strategies is gradually approaching that achieved by the best expert advices.Compared with the Universal Portfolio and the Exponential Gradient strategy,the proposed strategies can achieve more wealth and have better competitive performance.The proposed strategies and the comparative strategies own similar performance in the face of risk,and they are also sensitive to transaction costs in a similar extent.The results of numerical example also show that the more the number of stocks included in the portfolio,the better the improvement of the strategy based on combining the dynamic expert advices.This paper considers the actual situation to design online portfolio strategies.On the one hand,it can enrich the theory of online portfolio selection.On the other hand,it can provide investors with theoretical references for their investment decision-making activities.