Journal
INSURANCE MATHEMATICS & ECONOMICS
Volume 46, Issue 3, Pages 547-553Publisher
ELSEVIER
DOI: 10.1016/j.insmatheco.2010.02.001
Keywords
Tail condition expectation; Tail variance; Tail Mean-Variance model; Optimal portfolio selection; Square root of quadratic functional; Elliptical family; Quartic equation
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In the present paper we propose the Tail Mean-Variance (TMV) approach, based on Tail Condition Expectation (TCE) (or Expected Short Fall) and the recently introduced Tail Variance (TV) as a measure for the optimal portfolio selection. We show that, when the underlying distribution is multivariate normal, the TMV model reduces to a more complicated functional than the quadratic and represents a combination of linear, square root of quadratic and quadratic functionals. We show, however, that under general linear constraints, the solution of the optimization problem still exists and in the case where short selling is possible we provide an analytical closed form solution, which looks more robust than the classical MV solution. The results are extended to more general multivariate elliptical distributions of risks. (C) 2010 Elsevier B.V. All rights reserved.
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