原始-对偶投资组合优化问题的随机矩阵方法
Random matrix approach for primal-dual portfolio optimization problems
摘要：
本文在资产收益率方差相同的情况下，重新研究了在预算和投资集中度约束下投资风险最小化/最大化（原始问题）和在预算和投资风险约束下投资集中度最大化/最小化（对偶问题）的投资组合优化问题。我们用拉格朗日乘子法和随机矩阵法分析这两个优化问题。此后，我们比较从我们提出的方法与在以前的工作中获得的结果。此外，我们使用数值实验来验证从副本方法和随机矩阵方法作为分析原始和对偶投资组合优化问题的方法所获得的结果。
英文摘要：
In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by using the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.
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