Higher moment coherent risk measures

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66 Scopus citations


The paper considers modelling of risk-averse preferences in stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations that express risk measures via specially constructed stochastic programming problems. Using the developed representations, we introduce a new family of higher-moment coherent risk measures (HMCR), which includes, as a special case, the Conditional Value-at-Risk measure. It is demonstrated that the HMCR measures are compatible with the second order stochastic dominance and utility theory, can be efficiently implemented in stochastic optimization models, and perform well in portfolio optimization case studies.

Original languageEnglish (US)
Pages (from-to)373-387
Number of pages15
JournalQuantitative Finance
Issue number4
StatePublished - Aug 2007


  • Portfolio optimization
  • Risk measures
  • Stochastic dominance
  • Stochastic programming

ASJC Scopus subject areas

  • General Economics, Econometrics and Finance
  • Finance


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