集成有限个专家意见的在线投资组合策略

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.

Online portfolio selection strategy by aggregating finite expert advices

Based on the online learning character of weak aggregating algorithm (WAA), this paper explores its application to online portfolio selection, and considers the situation of making decision according to finite expert advices. The WAA is first applied to the expert strategies that invest only on one stock; then the single aggregating strategy (SAS) for online portfolio selection is obtained and the competitive performance of this strategy is analyzed, which shows SAS can pursue the best stock. In real investment decision-making, investors may choose several stocks to construct portfolios to invest, the WAA is further applied to the expert strategies that invest on different numbers of stocks; the mixture aggregating strategy (MAS) for online portfolio selection is then obtained; the conclusion that the cumulative gain MAS achieved is as large as that achieved by the best expert advice is proved. Numerical examples of long-period portfolios are provided to illustrate that SAS can achieve gain as well as the best stock; MAS can achieve gain as well as the best constant rebalanced portfolio (BCRP) strategy, and can obtain more when compared with universal portfolio (UP) strategy, which shows great competitive performance.