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Sensitivity Analysis in Applications with Deviation, Risk, Regret, and Error Measures
journal contribution
posted on 2018-03-13, 15:48 authored by Bogdan Grechuk, Michael ZabarankinThe 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.
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Citation
SIAM Journal on Optimization, 2017, 27(4), pp. 2481–2507Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- AM (Accepted Manuscript)
Published in
SIAM Journal on OptimizationPublisher
Society for Industrial and Applied Mathematicsissn
1052-6234eissn
1095-7189Acceptance date
2017-07-26Copyright date
2017Available date
2018-03-13Publisher DOI
Publisher version
https://epubs.siam.org/doi/10.1137/16M1105165Language
enAdministrator link
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