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In the present paper, the minimal investment risk for a portfoliooptimization problem with imposed budget and investment concentrationconstraints is considered using replica analysis. Since the minimal investmentrisk is influenced by the investment concentration constraint (as well as thebudget constraint), it is intuitive that the minimal investment risk for theproblem with an investment concentration constraint be larger than that withoutthe constraint (that is, with only the budget constraint). Moreover, anumerical experiment shows the effectiveness of our proposed analysis.

Minimal Investment Risk of Portfolio Optimization Problem with Budget and Investment Concentration Constraints