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Random matrix approach for primal-dual portfolio optimization problems

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  • Daichi Tada
  • Hisashi Yamamoto
  • Takashi Shinzato

Abstract

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.

Suggested Citation

  • Daichi Tada & Hisashi Yamamoto & Takashi Shinzato, 2017. "Random matrix approach for primal-dual portfolio optimization problems," Papers 1709.04620, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1709.04620
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    Cited by:

    1. Shinzato, Takashi, 2018. "Maximizing and minimizing investment concentration with constraints of budget and investment risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 986-993.

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