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Title: Spectral risk measures: the risk quadrangle and optimal approximation

We develop 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, we introduce an optimal approximation of spectral risk measures using quadrature. Lastly, we prove the consistency of this approximation and demonstrate our results through numerical examples.
Authors:
ORCiD logo [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
SAND-2018-5344J
Journal ID: ISSN 0025-5610; 663229
Grant/Contract Number:
AC04-94AL85000; NA0003525
Type:
Accepted Manuscript
Journal Name:
Mathematical Programming
Additional Journal Information:
Journal Name: Mathematical Programming; Journal ID: ISSN 0025-5610
Publisher:
Springer
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Stochastic optimization; Risk measures; Regression; Quadrature; Average value-at-risk
OSTI Identifier:
1441457

Kouri, Drew P. Spectral risk measures: the risk quadrangle and optimal approximation. United States: N. p., Web. doi:10.1007/s10107-018-1267-3.
Kouri, Drew P. Spectral risk measures: the risk quadrangle and optimal approximation. United States. doi:10.1007/s10107-018-1267-3.
Kouri, Drew P. 2018. "Spectral risk measures: the risk quadrangle and optimal approximation". United States. doi:10.1007/s10107-018-1267-3.
@article{osti_1441457,
title = {Spectral risk measures: the risk quadrangle and optimal approximation},
author = {Kouri, Drew P.},
abstractNote = {We develop 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, we introduce an optimal approximation of spectral risk measures using quadrature. Lastly, we prove the consistency of this approximation and demonstrate our results through numerical examples.},
doi = {10.1007/s10107-018-1267-3},
journal = {Mathematical Programming},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {5}
}