TY - JOUR
T1 - Sensitivity analysis in applications with deviation, risk, regret, and error measures
AU - Grechuk, Bogdan
AU - Zabarankin, Michael
N1 - Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Deviation measure
KW - Envelope theorem
KW - Error measure
KW - Portfolio optimization
KW - Risk measure
KW - Sensitivity analysis
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U2 - 10.1137/16M1105165
DO - 10.1137/16M1105165
M3 - Article
AN - SCOPUS:85040741443
SN - 1052-6234
VL - 27
SP - 2481
EP - 2507
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 4
ER -