TY - JOUR
T1 - Generalized deviations in risk analysis
AU - Rockafellar, R. Tyrrell
AU - Uryasev, Stan
AU - Zabarankin, Michael
PY - 2006/1
Y1 - 2006/1
N2 - 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.
AB - 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.
KW - Coherent risk measures
KW - Conditional value-at-risk
KW - Convex analysis
KW - Deviation measures
KW - Portfolio optimization
KW - Risk management
KW - Value-at-risk
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U2 - 10.1007/s00780-005-0165-8
DO - 10.1007/s00780-005-0165-8
M3 - Article
AN - SCOPUS:29144480897
SN - 0949-2984
VL - 10
SP - 51
EP - 74
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 1
ER -