Superquantiles and Their Applications to Risk, Random Variables, and Regression
dc.contributor.author | Rockafellar, R. Tyrrell | |
dc.contributor.author | Royset, Johannes O. | |
dc.date.accessioned | 2014-05-29T23:21:46Z | |
dc.date.available | 2014-05-29T23:21:46Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Tutorials in Operations Research, 2013 Informs | |
dc.identifier.uri | https://hdl.handle.net/10945/41716 | |
dc.description | The article of record as published may be found at http://dx.doi.org/10.1287 /educ.2013.0lll | en_US |
dc.description.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. | en_US |
dc.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. | en_US |
dc.title | Superquantiles and Their Applications to Risk, Random Variables, and Regression | en_US |
dc.type | Article | en_US |
dc.contributor.department | Operations Research | |
dc.subject.author | random variables | en_US |
dc.subject.author | quantiles | en_US |
dc.subject.author | superquantiles | en_US |
dc.subject.author | superexpectations | en_US |
dc.subject.author | superdistributions | en_US |
dc.subject.author | conjugate duality; | en_US |
dc.subject.author | stochastic dominance | en_US |
dc.subject.author | measures of risk | en_US |
dc.subject.author | value-at-risk | en_US |
dc.subject.author | conditional value-at-risk | en_US |
dc.subject.author | generalized regression | en_US |