Abstract:

For online portfolio selection problem, making full use of historical data can effectively reduce the impact of market noise on investment strategies, but it usually results in reduced their computational efficiency. Correspondingly, the increasing development of high-frequency trading and the explosive growth of data volume increasingly require investment strategies to have efficient computational ability. To this end, this paper proposes an online portfolio gradient descent strategy based on adaptive moment estimation, which makes use of historical data in an incremental manner with the help of adaptive moment estimation. The theoretical analysis shows that this strategy is universal, i.e., it has the same asymptotic average logarithmic growth rate as the offline best constant rebalanced portfolio. Meanwhile, this strategy still maintains linear time complexity while making full use of historical data. The empirical analysis shows that this strategy has a good performance in terms of the return and computational time metrics, and can sustain reasonable transaction costs. Therefore, it has good practical application prospects.

Key words:

online portfolio, universal portfolio, adaptive moment estimation, gradient descent

摘要：

对于在线投资组合选择问题，充分利用历史数据能有效地减少市场噪声对投资策略的影响，但这往往会导致策略计算效率降低。与其相对应的是，高频交易的日益发展与数据量的爆发式增长愈发要求投资策略具备高效的计算能力。为此，借助于自适应矩估计，以增量的方式利用历史数据，提出了一个基于自适应矩估计的在线投资组合梯度下降策略。理论分析表明，该策略具有泛证券性，即其与离线的最优定常再调整策略具有相同的渐近平均对数增长率；同时，该策略在充分利用历史数据的情况下依然保持线性时间复杂度。实证分析表明，该策略在收益以及计算时间等指标上表现出较好的性能，同时能承受合理的交易费用，故而具有良好的实际应用前景。

关键词:

在线投资组合, 泛证券投资组合, 自适应矩估计, 梯度下降