Cardinality-constrained distributionally robust portfolio optimization
Cardinality-constrained distributionally robust portfolio optimization
复制标题
基数约束的分布鲁棒投资组合优化
DOI：
10.1016/j.ejor.2023.01.037
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发表时间：
2023
影响因子：
6.4
通讯作者：
Kazuhide Nakata
中科院分区：
文献类型：
--
作者：
Ken Kobayashi;Yuichi Takano;Kazuhide Nakata
研究了一个具有基数约束的分布鲁棒投资组合优化模型。我们制定了这个模型作为一个混合整数半定优化（MISDO）的问题，通过基于矩的模糊集的资产收益率的概率分布。为了精确求解大规模问题，提出了一种基于双层优化重构的割平面算法。我们证明了算法的有限收敛性。我们还将矩阵完成技术应用于较低级别的SDO问题，使其问题的规模小得多。数值实验表明，我们的切割平面算法是显着快于国家的最先进的MISDO求解器SCIP-SDP。我们还表明，我们的投资组合优化模型可以实现良好的投资绩效相比，传统的鲁棒优化模型的基础上的椭球不确定性集。
This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by means of the moment-based ambiguity set of probability distributions of asset returns. To exactly solve large-scale problems, we propose a specialized cutting-plane algorithm that is based on bilevel optimization reformulation. We prove the finite convergence of the algorithm. We also apply a matrix completion technique to lower-level SDO problems to make their problem sizes much smaller. Numerical experiments demonstrate that our cutting-plane algorithm is significantly faster than the state-of-the-art MISDO solver SCIP-SDP. We also show that our portfolio optimization model can achieve good investment performance compared with the conventional robust optimization model based on the ellipsoidal uncertainty set.