This paper presents a general sparse portfolio selection model with expectation, chance and cardinality constraints. For the sparse portfolio selection model, we derive respectively the sample based reformulation and distributionally robust reformulation with mixture distribution based ambiguity set. These reformulations are mixed-integer programming problem and programming problem with difference of convex functions (DC), respectively. As an application of the general model and its reformulations, we consider the sparse enhanced indexation problem with multiple constraints. Empirical tests are conducted on the real data sets from major international stock markets. The results demonstrate that the proposed model, the reformulations and the solution method can efficiently solve the enhanced indexation problem and our approach can generally achieve sparse tracking portfolios with good out-of-sample excess returns and high robustness.

本文提出了一个具有期望，机会和基数约束的通用稀疏投资组合选择模型。对于稀疏的投资组合选择模型，我们分别推导了基于样本的重构和基于混合分布的歧义集的分布鲁棒重构。这些重构分别是混合整数编程问题和具有凸函数（DC）差异的编程问题。作为通用模型及其重构的一种应用，我们考虑了具有多个约束的稀疏增强索引问题。对来自主要国际股票市场的真实数据集进行了实证检验。结果表明，提出的模型