Sensitivity analysis in applications with deviation, risk, regret, and error measures

Bogdan Grechuk, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 Lp-type and semi-Lp 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.

Original languageEnglish
Pages (from-to)2481-2507
Number of pages27
JournalSIAM Journal on Optimization
Volume27
Issue number4
DOIs
StatePublished - 2017

Keywords

  • Deviation measure
  • Envelope theorem
  • Error measure
  • Portfolio optimization
  • Risk measure
  • Sensitivity analysis

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