Excess invariance and shortfall risk measures

Jeremy Staum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper introduces the axiom of excess invariance for risk measures, meaning insensitivity to the amount by which a portfolio's value exceeds a benchmark. Using this axiom, the paper defines the class of shortfall risk measures. Shortfall risk measures are suitable for regulatory or risk management applications in which risk is associated with shortfall beneath a benchmark, whereas excess above the benchmark is not important.

Original languageEnglish (US)
Pages (from-to)47-53
Number of pages7
JournalOperations Research Letters
Issue number1
StatePublished - Jan 2013


  • Cash additive
  • Cash invariant
  • Excess-invariant
  • Risk measures
  • Shortfall
  • Translation invariant

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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