Spectral risk measures: the risk quadrangle and optimal approximation
type: Item
instance of: scholarly article
title: Spectral risk measures: the risk quadrangle and optimal approximation
zbMATH Open document ID: 1470.91332
author: D. P. Kouri
published in: Mathematical Programming. Series A. Series B
publication date: 2019-04-24T00:00:00Z
full work available at URL: https://www.osti.gov/biblio/1441457
review text: Countless science and engineering decisions are formulated as optimization problems, many of which are riddled with uncertainty. For such problems, it is critical that the optimal solutions not only account for, but are resilient to this uncertainty. Risk measures provide a convenient utility for quantifying the hazard associated with random objectives and constraints. The risk quadrangle provides a rigorous connection between statistical estimation and risk-averse optimization by furnishing fundamental relationships connecting regular measures of risk, deviation, error and regret. The author develops a general risk quadrangle that gives rise to a large class of spectral risk measures. The statistic of this new risk quadrangle is the average value-at-risk at a specific confidence level. As such, this risk quadrangle generates a continuum of error measures that can be used for superquantile regression. For risk-averse optimization, an optimal approximation of spectral risk measures is introduced using quadrature. The consistency of this approximation is proved. Numerical examples are presented with a problem of optimal contaminant mitigation.
reviewed by: Martin Gugat
Mathematics Subject Classification ID: 91G70
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 91B05
zbMATH DE Number: 7047601
zbMATH Keywords: stochastic optimization
zbMATH Keywords: risk measures
zbMATH Keywords: regression
zbMATH Keywords: quadrature
zbMATH Keywords: average value-at-risk
zbMATH Keywords: risk quadrangle
MaRDI profile type: Publication
OpenAlex ID: W2803669158
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Wikidata QID: Q129778914
DOI: 10.1007/S10107-018-1267-3
description: scientific article; zbMATH DE number 7047601