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基于弱集成算法的在线学习特征,该文探讨了它在在线投资组合选择中的应用,考虑了根据有限个专家意见进行决策的情形.首先将弱集成算法应用到投资于单只股票的专家意见,得到了在线投资组合的单一集成策略,并给出了该策略的竞争性能分析,证明了单一集成策略能够追踪最好的股票,实际投资决策中,投资者可能会选择多只股票进行组合投资,进一步将弱集成算法应用到投资于不同股票数目的专家意见,得到了在线投资组合的混合集成策略;证明了混合集成策略实现的累积收益与最优专家意见实现的累积收益相当.在长期投资组合上的数值算例表明了该文给出的单一集成策略能够实现与最好股票相当的收益;混合集成策略能够实现与最优定常再调整策略相当的收益,且与泛证券投资组合策略相比,能够获得更多的收益,具有较好的竞争性能.
Based on the online learning characteristics of weak integration algorithm, this paper discusses its application in online portfolio selection and considers the case of making decisions based on a limited number of expert opinions.First, the weak integration algorithm is applied to the expert opinion of investing in a single stock , A single integrated strategy of online portfolio is obtained and the competitive performance analysis of the strategy is given. It is proved that a single integrated strategy can track the best stocks. In actual investment decisions, investors may choose multiple stocks for portfolio investment , The weak integration algorithm is further applied to the expert opinion of investing in different stocks, and the hybrid integration strategy of online portfolio is obtained. It is proved that the cumulative benefits achieved by the hybrid integration strategy are equal to the cumulative benefits of the optimal expert opinion. The numerical example on the portfolio shows that the single integrated strategy presented in this paper can achieve the best return on the stock market. The hybrid integrated strategy can achieve the return equivalent to the optimal steady-state readjustment strategy, Than can get more revenue, with better competitive performance.