Spectral risk measures: the risk quadrangle and optimal approximation
成果类型：
Article
署名作者：
Kouri, Drew P.
署名单位：
United States Department of Energy (DOE); Sandia National Laboratories
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-018-1267-3
发表日期：
2019
页码：
525-552
关键词：
摘要：
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. We prove the consistency of this approximation and demonstrate our results through numerical examples.