Publication:
Superquantiles and Their Applications to Risk, Random Variables, and Regression

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Authors
Rockafellar, R. Tyrrell
Royset, Johannes O.
Subjects
random variables
quantiles
superquantiles
superexpectations
superdistributions
conjugate duality;
stochastic dominance
measures of risk
value-at-risk
conditional value-at-risk
generalized regression
Advisors
Date of Issue
2013
Date
Publisher
Language
Abstract
Superquantiles (also called conditional values-at-risk) are useful tools in risk modeling and optimization, with expanding roles beyond these areas. This tutorial provides a broad overview of superquantiles and their versatile applications. We see that superquantiles are as fundamental to the description of a random variable as the cumulative distribution function (cdf), they can recover the corresponding quantile function through differentiation, they are dual in some sense to superexpectations, which are convex functions uniquely defining the cdf, and they also characterize convergence in distribution. A superdistribution function defined by superquantiles leads to higher-order superquantiles as well as new measures of risk and error, with important applications in risk modeling and generalized regression.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1287 /educ.2013.0lll
Series/Report No
Department
Operations Research
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Tutorials in Operations Research, 2013 Informs
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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