带交易成本的二阶在线投资组合选择策略

Second-order online portfolio selection strategy with transaction costs

针对基于在线牛顿步(Online Newton Step, ONS)算法的投资组合选择策略没有考虑交易成本的问题,而交易成本是真实市场中不可或缺的部分,提出了一种新的带交易成本的在线投资组合选择策略,简称在线牛顿步交易成本策略(Online Newton Step Transaction Cost,ONSC):首先,结合投资组合向量的二阶信息和交易成本惩罚项构造优化函数,并推导得出投资组合的更新公式;然后,通过理论分析得到ONSC算法的次线性后悔边界O(log(T)).实证研究表明,与半常数再调整投资组合策略(Semiconstant Rebalanced Portfolios, SCRP)以及其他考虑交易成本的策略相比,在SP500、NYSE(O)、NYSE(N)和TSE这4个真实市场的数据集上,ONSC获得了最高的累计净收益和最小的周转率,表明了所提算法的有效性.

Existing portfolio selection strategies based on the online Newton step (ONS) algorithm ignore the role of transaction costs,an indispensable factor in real markets.This paper proposes a new online portfolio selection strategy,the online Newton step transaction cost (ONSC) method,to address this issue.First,we constructed the optimal function by combining second order information of a portfolio with the transaction cost penalty term,and the portfolio was subsequently updated.Then,the sublinear regret bound O(log(T)) was achieved by theoretical analysis.Empirical research on the data sets of four real markets-namely,SP500,NYSE(O),NYSE(N) and TSE-showed that in comparison to semiconstant rebalanced portfolios (SCRP) and other strategies with transaction costs,ONSC achieves the highest accumulated wealth and the smallest turnover.Hence,the research demonstrates the effectiveness of the algorithm.