基于排序预测的带交易费用在线投资组合策略

在线投资组合决策过程中频繁调整资产头寸会产生较多的交易费用。本文提出了一个综合考虑预期收益和交易费用的在线投资组合策略。通过预测资产的排序计算组合的预期收益,利用相对熵距离衡量交易费用,构造了一个极大化预期收益和极小化交易费用的优化模型,从而得到了一个在线投资组合更新策略。然后,从理论上证明了该策略具有BH泛证券性,即该策略与离线的最优购买并持有策略具有相同的渐近平均指数收益率。最后,采用中美股票市场实际数据,对该策略进行了数值分析。结果表明,该策略的表现优于已有的在线投资组合策略,且对模型的参数不敏感。

Online Portfolio Strategy Based on Order Prediction with Transaction Costs

During the process of online portfolio decision-making, frequent adjustments of asset positions will cause a lot of transaction costs. This paper proposes an online portfolio strategy by considering both expected return and transactioncosts. We calculate the expected return of the portfolio by predicting the order of assets and measure the transaction costs by using the relative entropy distance, and thus construct an optimization model thatmaximizes the expected return and minimizes the transaction costs, and then obtain an online portfolio update strategy by solving it. Then, we theoretically prove that the strategy has BH-universality, that is, its average exponential growth rate is asymptotically the same as that of the offline optimal Buy and Hold strategy. Finally, we conduct numerical analysis of the proposed strategy on actual stock data from Chinese and American markets. The results show that it achieves a better cumulative wealth than the existing online portfolio strategies and is not sensitive to the parameters of the model.