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The portfolio optimization problem in which the variances of the return ratesof assets are not identical is analyzed in this paper using the methodology ofstatistical mechanical informatics, specifically, replica analysis. We definetwo characteristic quantities of an optimal portfolio, namely, minimalinvestment risk and concentrated investment level, in order to solve theportfolio optimization problem and analytically determine their asymptoticalbehaviors using replica analysis. Moreover, numerical experiments wereperformed, and a comparison between the results of our simulation and thoseobtained via replica analysis validated our proposed method.

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