Research On Online Portfolio Selection Strategy Based On Learning With Expert Advice Considering Side Information

With the development of economy and the improvement of residents' disposable income,people's demand for investment and wealth management is increasing day by day.Different from the traditional mean-variance model,the online portfolio selection model is a sequential decision-making model.Investors do not need to make any probabilistic assumptions about asset prices,but only use the current information to make decisions.There is a lot of information in the financial market that is helpful for investment decision-making.This thesis introduces this information into the online portfolio problem,and proposes three online portfolio strategies considering side information.Firstly,this thesis proposes an online portfolio strategy based on linear learning function considering side information.This strategy is to adjust the portfolio based on the portfolio of the latest period with the same side information state as the current period and increase the investment weights of stocks with good performance in the period,and then more funds will be put in stocks with good performance.Considering that the stock market is changing rapidly and only considering the performance of a single period may cause investment income instability.Therefore,this thesis considers the cumulative wealth under the same side information in the past as the basis of weight distribution,and proposes an online portfolio selection strategy by learning with the advice of limited experts considering side information.Firstly,the strategies of investing in the same single stock under the same side information state and possibly investing in different single stocks under different side information states are regarded as experts.This thesis uses the exponentially weighted average algorithm to comprehensively consider the expert advice and gives greater weight to the experts with better cumulative wealth under the same side information state in the past.Furthermore,the finite number of experts is extended to the infinite number of experts.The strategies that adopt the same investment decision under the same side information state and may adopt different investment decisions under different side information states are regarded as experts,and an online portfolio selection strategy by learning with the advice of infinite experts considering side information is constructed.Then,the competitive performance of the three strategies is analyzed theoretically,and it is proved that the strategies have theoretical guarantee.Then,we use the real stock price data of the Chinese and American markets to analyze the three strategies numerically,and measure the performance of the strategies through multiple indicators,such as final cumulative wealth,daily cumulative wealth,etc.,and compare it with other online and offline strategies to further measure the competitiveness of the strategies.This thesis considers side information into the online portfolio selection problem,which can effectively guide investors to make investment decisions and enrich the research results in the field of online portfolio selection problem.At the same time,guiding investors to make rational investment can indirectly contribute to the stable development of financial market.