Generalized deviations in risk analysis

R. Tyrrell Rockafellar, Stan Uryasev, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

346 Scopus citations

Abstract

General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their properties are explored with a mind to generating a large assortment of examples and assessing which may exhibit superior behavior. Connections are shown with coherent risk measures in the sense of Artzner, Delbaen, Eber and Heath, when those are applied to the difference between a random variable and its expectation, instead of to the random variable itself. However, the correspondence is only one-to-one when both classes are restricted by properties called lower range dominance, on the one hand, and strict expectation boundedness on the other. Dual characterizations in terms of sets called risk envelopes are fully provided.

Original languageEnglish
Pages (from-to)51-74
Number of pages24
JournalFinance and Stochastics
Volume10
Issue number1
DOIs
StatePublished - Jan 2006

Keywords

  • Coherent risk measures
  • Conditional value-at-risk
  • Convex analysis
  • Deviation measures
  • Portfolio optimization
  • Risk management
  • Value-at-risk

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