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


  • Z. Landsman
  • U. Makov


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.

Suggested Citation

  • Z. Landsman & U. Makov, 2011. "Translation-invariant and positive-homogeneous risk measures and optimal portfolio management," The European Journal of Finance, Taylor & Francis Journals, vol. 17(4), pages 307-320.
  • Handle: RePEc:taf:eurjfi:v:17:y:2011:i:4:p:307-320
    DOI: 10.1080/1351847X.2010.481467

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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.
    2. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS
    3. repec:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0856-z is not listed on IDEAS


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