Translation-invariant and positive-homogeneous risk measures and optimal portfolio management in the presence of a riskless component

Zinoviy Landsman, Udi Makov

Research output: Contribution to journalArticlepeer-review

Abstract

Risk portfolio optimization, with translation-invariant and positive-homogeneous risk measures, 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.This problem was recently treated by the authors for the case when the portfolio does not contain a riskless component. When it does, however, the initial covariance matrix σ becomes singular and the problem becomes more complicated. In the paper we focus on this case and provide an explicit closed-form solution of the minimization problem, and the condition under which this solution exists. The results are illustrated using data of 10 stocks from the NASDAQ Computer Index.

Original languageEnglish
Pages (from-to)94-98
Number of pages5
JournalInsurance: Mathematics and Economics
Volume50
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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