Shinzato Takashi
Mori Arinori Center for Higher Education and Global Mobility, Hitotsubashi University, Tokyo, 1868601, Japan.
Phys Rev E. 2016 Dec;94(6-1):062102. doi: 10.1103/PhysRevE.94.062102. Epub 2016 Dec 1.
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.
本文运用统计力学信息学方法，特别是复制分析，对资产回报率方差不相同情况下的投资组合优化问题进行了分析。为了解决投资组合优化问题，我们定义了最优投资组合的两个特征量，即最小投资风险和投资集中度，并通过复制分析解析地确定了它们的渐近行为。我们还进行了数值实验，模拟结果与通过复制分析得到的结果之间的比较验证了我们提出的方法。
