Equivalent distortion risk measures on moment spaces

Dries Cornilly, Steven Vanduffel

Research output: Contribution to journalArticlepeer-review


We show that maximizing distortion risk measures over the set of distributions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.

Original languageEnglish
Pages (from-to)187-192
Number of pages6
JournalStatistics and Probability Letters
Publication statusPublished - 1 Mar 2019


  • Coherent risk measure
  • Distortion function
  • Expected shortfall (ES)
  • Model uncertainty
  • Value-at-Risk (VaR)


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