Optimality Conditions in Portfolio Analysis with General Deviation Measures

University of Florida Industrial and Systems Engineering Working Paper No. 2004-7

23 Pages Posted: 9 Nov 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: May 10, 2005

Abstract

Optimality conditions are derived for problems of minimizing a generalized measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. Generalized measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality conditions are applied to characterize the generalized master funds which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation. The consequences are worked out for deviation based on conditional value-at-risk and its variants, in particular.

Keywords: Generalized deviation measures, portfolio analysis, generalized master funds, CAPM-like relations, optimality conditions, risk envelopes, risk identifiers, conditional value-at-risk, risk management, stochastic optimization

JEL Classification: C0, C2, C6

Suggested Citation

Rockafellar, R. Tyrrell and Uryasev, Stanislav P. and Zabarankin, Michael, Optimality Conditions in Portfolio Analysis with General Deviation Measures (May 10, 2005). University of Florida Industrial and Systems Engineering Working Paper No. 2004-7, Available at SSRN: https://ssrn.com/abstract=615581 or http://dx.doi.org/10.2139/ssrn.615581

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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