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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 and M. M\'ezard [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, 2010. "Belief Propagation Algorithm for Portfolio Optimization Problems," Papers 1008.3746, arXiv.org, revised Sep 2010.
    • Handle: RePEc:arx:papers:1008.3746
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    Cited by:

    1. Takashi Shinzato, 2014. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," Papers 1404.5222, arXiv.org, revised Apr 2014.
    2. 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.

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