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Portfolio optimization based on divergence measures

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  • Chalabi, Yohan
  • Wuertz, Diethelm
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    Abstract

    A new portfolio selection framework is introduced where the investor seeks the allocation that is as close as possible to his "ideal" portfolio. To build such a portfolio selection framework, the f-divergence measure from information theory is used. There are many advantages to using the f-divergence measure. First, the allocation is made such that it is in agreement with the historical data set. Second, the divergence measure is a convex function, which enables the use of fast optimization algorithms. Third, the objective value of the minimum portfolio divergence measure provides an indication distance from the ideal portfolio. A statistical test can therefore be constructed from the value of the objective function. Fourth, with adequate choices of both the target distribution and the divergence measure, the objective function of the f-portfolios reduces to the expected utility function.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43332.

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    Date of creation: Nov 2012
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    Handle: RePEc:pra:mprapa:43332

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    Related research

    Keywords: Portfolio weights modeling; Divergence measures; Dual divergence; Information theory; Minimax optimization problems;

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    1. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    2. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
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    7. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    8. Toma, Aida & Leoni-Aubin, Samuela, 2010. "Robust tests based on dual divergence estimators and saddlepoint approximations," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1143-1155, May.
    9. Stutzer, Michael, 1996. " A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-52, December.
    10. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    11. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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