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Translation-invariant and positive-homogeneous risk measures and optimal portfolio management


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  • Z. Landsman
  • U. Makov
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    The problem of risk portfolio optimization with translation-invariant and positive-homogeneous risk measures, which includes value-at-risk (VaR) and tail conditional expectation (TCE), leads to the problem of minimizing a combination of a linear functional and a square root of a quadratic functional for the case of elliptical multivariate underlying distributions. In this paper, we provide an explicit closed-form solution of this minimization problem, and the condition under which this solution exists. The results are illustrated using the data of 10 stocks from NASDAQ/Computers. The distance between the VaR and TCE optimal portfolios has been investigated.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

    Volume (Year): 17 (2011)
    Issue (Month): 4 ()
    Pages: 307-320

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    Handle: RePEc:taf:eurjfi:v:17:y:2011:i:4:p:307-320

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    Keywords: translation-invariant and positive-homogeneous risk measure; value-at-risk; tail condition expectation; minimization of root of quadratic functional; elliptical family;


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    Cited by:
    1. Landsman, Zinoviy & Makov, Udi, 2012. "Translation-invariant and positive-homogeneous risk measures and optimal portfolio management in the presence of a riskless component," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 94-98.


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