A rescaling technique to improve numerical stability of portfolio optimization problems
A rescaling technique to improve numerical stability of portfolio optimization problems
复制标题
提高投资组合优化问题数值稳定性的重新缩放技术
DOI：
10.1007/s00500-021-06543-1
复制
发表时间：
2022
期刊：
影响因子：
4.1
通讯作者：
P. Uberti
中科院分区：
文献类型：
--
作者：
M. Torrente;P. Uberti
本文分析了Markowitz投资组合优化模型的数值稳定性，通过识别和研究不稳定性的来源，该来源严格依赖于优化问题的数学结构及其约束条件。因此，它示出了如何标准的投资组合优化模型也可以导致在一个不稳定的模型时，协方差矩阵是良好的条件和目标函数是数值稳定的。这取决于模型的线性等式约束经常遭受几乎共线性和/或不良缩放的事实。提出了一种理论方法，利用原优化问题的等效制定大大减少了这种结构组件的不稳定性。当需要数值优化方法来计算最优投资组合时，通过对真实的金融数据的应用，经验证明了该建议的有效性。比较了Guidelines和MATLAB的solversquadprograndfmincons的收敛性能。
This paper analyzes the numerical stability of Markowitz portfolio optimization model, by identifying and studying a source of instability, that strictly depends on the mathematical structure of the optimization problem and its constraints. As a consequence, it is shown how standard portfolio optimization models can result in an unstable model also when the covariance matrix is well conditioned and the objective function is numerically stable. This depends on the fact that the linear equality constraints of the model very often suffer of almost collinearity and/or bad scaling. A theoretical approach is proposed that exploiting an equivalent formulation of the original optimization problem considerably reduces such structural component of instability. The effectiveness of the proposal is empirically certified through applications on real financial data when numerical optimization approaches are needed to compute the optimal portfolio. Gurobi and MATLAB’s solversquadprogandfminconare compared in terms of convergence performances.