标题： 基于统计机械信息学的具有不同资产收益方差的投资组合优化问题 显示英文标题

标题： Portfolio Optimization Problem with Non-identical Variances of Asset Returns using Statistical Mechanical Informatics

摘要： 在本文中，使用统计机械信息学的方法，特别是副本分析法，分析了资产收益率方差不相同的组合优化问题。 为了求解组合优化问题，并通过副本分析法解析地确定其渐近行为，我们定义了最优组合的两个特征量，即最小投资风险和集中投资水平。 此外，进行了数值实验，并将我们的模拟结果与通过副本分析获得的结果进行比较，验证了我们提出的方法。 显示英文摘要

摘要： 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 define two characteristic quantities of an optimal portfolio, namely, minimal investment risk and concentrated investment level, in order to solve the portfolio optimization problem and analytically determine their asymptotical behaviors using replica analysis. Moreover, numerical experiments were performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.