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# Sensitivity Analysis in Applications with Deviation, Risk, Regret, and Error Measures

journal contribution
posted on 13.03.2018, 15:48 by Bogdan Grechuk, Michael Zabarankin
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.

## Citation

SIAM Journal on Optimization, 2017, 27(4), pp. 2481–2507

## Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

## Version

AM (Accepted Manuscript)

## Published in

SIAM Journal on Optimization

## Publisher

Society for Industrial and Applied Mathematics

1052-6234

1095-7189

26/07/2017

2017

13/03/2018

## Publisher version

https://epubs.siam.org/doi/10.1137/16M1105165

en