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

作　　者：张鑫熔 彭深 ZHANG Xinrong;PENG Shen(School of Mathematics and Statistics,Xidian University,Xi′an 710071,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《纯粹数学与应用数学》2023年第3期437-454,共18页Pure and Applied Mathematics

基　　金：国家自然科学基金(12271419);陕西省自然科学基金青年项目(2023-JC-QN-0081);中央高校自由探索青年项目(XJS220706)。

摘　　要：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.

关 键 词：投资组合选择 高阶矩优化 基数约束 牛顿算法 样本外分析 

分 类 号：O221.2[理学—运筹学与控制论]