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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)307-320
Number of pages14
JournalEuropean Journal of Finance
Issue number4
StatePublished - Apr 2011


  • Elliptical family
  • Minimization of root of quadratic functional
  • Tail condition expectation
  • Translation-invariant and positive-homogeneous risk measure
  • Value-at-risk

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)


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