带交易费用的集成专家意见在线投资组合策略

在多期投资组合选择过程中,频繁调整投资比例将会产生一系列的交易费用,是影响投资决策的一个重要因素.在线投资组合属于多期投资组合;投资比例需要按照投资期数逐步调整,而不是一次性确定的.本文将交易费用引入到在线投资组合模型中,应用集成有限个专家意见的弱集成算法设计在线投资组合策略.首先探讨了专家意见为在每阶段都固定地投资于单只股票的情形,得到了考虑交易费用的单一集成策略,证明了与最优专家意见相比,他们的累积收益平均值之间的差值存在渐进形式的下界.其次,讨论了专家意见为在每阶段都固定地投资于多只股票的情形,得到了带交易费用的混合集成策略,并给出了该策略的竞争性能分析.基于纽约证券交易所的股票数据,数值算例进一步说明了本文给出的带交易费用的单一集成策略和混合集成策略几乎与最优专家意见的性能一样好,并分析了交易费用对策略性能的影响.

Online portfolio selection strategy of aggregating expert advice with transaction costs

In the process of multi-period portfolio selection, the frequent adjustment of investment proportion will produce a series of transaction costs, which is an important factor affecting the decision-making of investment. Online portfolio belongs to the multi-period portfolio; the proportion of investment needs to be adjusted in accordance with the investment stage, rather than a one-time determination. This paper introduces the transaction costs into the online portfolio model, and further applies the weak aggregating algorithm to integrated finite expert advice to design online portfolio strategy. Firstly, this paper discusses the situation that expert advice is fixedly investing on single stock at every period and obtains the single aggregating strategy with transaction costs; and proves the conclusion that comparing with best expert, there exists asymptotical lower bound on the difference between their average cumulative gains. Secondly, this paper discusses the situation that the expert advice is fixedly investing on different numbers of stocks at every period, and obtains the mixed aggregating strategy with transaction costs, and provides the competitive performance of this strategy. Based on the transaction data of New York stock market, numerical examples are given to prove that the single aggregating strategy and mixed aggregating strategy with transaction costs can achieve almost the same performance as the best expert advice, and the effect of transaction costs on strategies' performance is also analyzed.