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Title: Sensitivity Analysis in Applications with Deviation, Risk, Regret, and Error Measures
Authors: Grechuk, Bogdan
Zabarankin, Michael
First Published: 19-Dec-2017
Publisher: Society for Industrial and Applied Mathematics
Citation: SIAM Journal on Optimization, 2017, 27(4), pp. 2481–2507
Abstract: The envelope formula is obtained for optimization problems with positively homogeneous convex functionals defined on a space of random variables. Those problems include linear regression with general error measures and optimal portfolio selection with the objective function being either a general deviation measure or a coherent risk measure subject to a constraint on the expected rate of return. The obtained results are believed to be novel even for Markowitz's mean-variance portfolio selection but are far more general and include explicit envelope relationships for the rates of return of portfolios that minimize lower semivariance, mean absolute deviation, deviation measures of ${\cal L}^p$-type and semi-${\cal L}^p$ type, and conditional value-at-risk. In each case, the envelope theorem yields explicit estimates for the absolute value of the difference between deviation/risk of optimal portfolios with the unperturbed and perturbed asset probability distributions in terms of a norm of the perturbation.
DOI Link: 10.1137/16M1105165
ISSN: 1052-6234
eISSN: 1095-7189
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s open access archiving policy. (
Appears in Collections:Published Articles, Dept. of Mathematics

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