Generalized deviations in risk analysis
R. Rockafellar (rtr@math.washington.edu),
Stan Uryasev (uryasev@ufl.edu) and
Michael Zabarankin (mzabaran@stevens.edu)
Finance and Stochastics, 2006, vol. 10, issue 1, 74 pages
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. Copyright Springer-Verlag Berlin/Heidelberg 2006
Keywords: Risk management; deviation measures; coherent risk measures; value-at-risk; conditional value-at-risk; portfolio optimization; convex analysis (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:10:y:2006:i:1:p:51-74
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DOI: 10.1007/s00780-005-0165-8
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