Optimality conditions in portfolio analysis with general deviation measures

Authors:
R. Tyrrell Rockafellar;Stan Uryasev;Michael Zabarankin
Affiliations:
Department of Mathematics, University of Washington, Box 354350, 98195-4350, Seattle, WA, USA;Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, 303 Weil Hall, 32611-6595, Gainesville, FL, USA;Department of Mathematical Sciences, Stevens Institute of Technology, P.O. Box 116595, Castle Point on Hudson, 07030, Hoboken, NJ, USA
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

Optimality conditions are derived for problems of minimizing a general 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. General 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.