求解稀疏高阶矩投资组合问题的混合启发式算法

An efficient hybrid heuristic algorithm for sparse portfolio optimization with higher-order moment

本文旨在针对带有基数约束的高阶矩投资组合优化模型,设计一种高效的混合启发式求解算法.具体地,首先构建一个带有l_(2)正则化的均值-方差-偏度模型,并且提出了一个具有全局收敛性的Cubic-Newton算法.然后,进一步考虑基数约束下的模型求解,提出了一种改进的混合启发式算法,其中适应值的计算嵌入了Cubic-Newton算法,以改善迭代种群的质量.最后,利用OR-Library的6个标准数据集进行实证分析,并以样本外夏普比率,样本内外一致性为评价指标.实验结果表明本文提出方法普遍优于等权重投资策略,均值-方差(MV)投资组合策略以及稀疏均值-方差(SMV)投资组合策略.

In this paper,we propose an efficient hybrid heuristic algorithm to solve the higher-order moment portfolio optimization model with cardinality constraint.Specifically,we first introduce an l_(2)-regularized mean-variance-skewness model and establish a cubic regularization Newton(CR-Newton)algorithm with global convergence.We further consider a cardinality-constrained portfolio selection model.An improved hybrid heuristic method restricted to a genetic algorithm framework is proposed,into which the CR-Newton algorithm is embedded to improve the quality of the iterative population.The empirical analysis on six standard data sets from OR-library show that our proposed method is generally superior to the naive evenly weighted strategy,the mean-variance(MV)portfolio strategy,and the sparse mean-variance(SMV)portfolio strategy in terms of the out-of-sample Sharpe ratio and the consistency between in-sample and out-of-sample performance.