基于L_(1,1/2)的组稀疏投资选择模型

Group Sparse Portfolio Selection Model Based on L_(1,1/2)

组稀疏投资选择问题是目前金融学领域里十分核心和活跃的课题之一。这一问题的研究和解决需要在一个跨学科的平台上进行,通过应用统计估计、最优化理论、矩阵分析和经济学等学科知识,结合分块矩阵的思想,采用对比、分析、归纳等方法,从而取得了较为丰富的研究成果。本文在Markowitz开创的理性投资者进行资产组合的理论和方法的基础上,基于L1,1/2正则化理论,构建了组稀疏投资选择模型,得出了数值求解这类模型的Half阈值算法。

Group sparse investment selection is one of the core and active topics in the field of finance. The research and resolution of this problem needs to be carried out on an interdisciplinary platform through the application of statistical estimation, optimization theory,matrix analysis. Combining with the knowledge of economics and other disciplines, combined with the idea of block matrix, using contrast,analysis, induction and other methods, thus obtaining rich research results. Based on the theory and method of asset portfolio of rational investors pioneered by Markowitz, based on the L1,1/2 regularization theory, this paper constructs a group sparse investment selection model and obtains the Half threshold algorithm for numerically solving such models.