Generalized Deviations in Risk Analysis

University of Florida Department of Industrial and Systems Engineering Working Paper No. 2004-4

22 Pages Posted: 10 Sep 2004

See all articles by R. Tyrrell Rockafellar

R. Tyrrell Rockafellar

University of Washington - Department of Mathmatics

Stanislav P. Uryasev

University of Florida

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: September 3, 2004

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.

Keywords: Risk management, deviation measures, coherent risk measures

JEL Classification: C00, C60, C70

Suggested Citation

Rockafellar, R. Tyrrell and Uryasev, Stanislav P. and Zabarankin, Michael, Generalized Deviations in Risk Analysis (September 3, 2004). University of Florida Department of Industrial and Systems Engineering Working Paper No. 2004-4, Available at SSRN: https://ssrn.com/abstract=587441 or http://dx.doi.org/10.2139/ssrn.587441

R. Tyrrell Rockafellar

University of Washington - Department of Mathmatics ( email )

Box 354350
Seattle, WA 98195-4350
United States

Stanislav P. Uryasev (Contact Author)

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)

HOME PAGE: http://www.ise.ufl.edu/uryasev/

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://personal.stevens.edu/~mzabaran/

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