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Belief Propagation Algorithm for Portfolio Optimization Problems

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  • Takashi Shinzato
  • Muneki Yasuda

Abstract

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

Suggested Citation

  • Takashi Shinzato & Muneki Yasuda, 2015. "Belief Propagation Algorithm for Portfolio Optimization Problems," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-10, August.
    • Handle: RePEc:plo:pone00:0134968
    DOI: 10.1371/journal.pone.0134968
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    References listed on IDEAS

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    1. Takashi Shinzato, 2015. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-24, July.
    2. S. Ciliberti & M. Mézard, 2007. "Risk minimization through portfolio replication," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 175-180, May.
    3. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
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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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