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Belief Propagation Algorithm for Portfolio Optimization Problems

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  • Takashi Shinzato
  • Muneki Yasuda
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    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.

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    File URL: http://arxiv.org/pdf/1008.3746
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1008.3746.

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    Date of creation: Aug 2010
    Date of revision: Sep 2010
    Handle: RePEc:arx:papers:1008.3746

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