Superquantiles and Their Applications to Risk, Random Variables, and Regression
Rockafellar, R. Tyrrell
Royset, Johannes O.
MetadataShow full item record
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.
The article of record as published may be found at http://dx.doi.org/10.1287 /educ.2013.0lll
Showing items related by title, author, creator and subject.
Royset, Johannes O.; Rockafellar, R. Tyrrell (2015-11-05);Superquantiles, which refer to conditional value-at-risk (CVaR) in the same way that quantiles refer to value-at-risk (VaR), have many advantages in the modeling of risk in finance and engineering. However, some applications ...
Superquantile Regression with Applications to Buffered Reliability, Uncertainty Quantification, and Conditional Value-at-Risk Rockafellar, R.T.; Royset, J.O.; S.I. Miranda (2013-08-03);The paper presents a generalized regression technique centered on a superquantile (also called conditional value-at-risk) that is consistent with that coherent measure of risk and yields more conservatively fitted curves ...
Sabol, John J., III (Monterey, California: Naval Postgraduate School, 2016-06);Analysts often concern themselves with the tail regions of distributions, sometimes called extreme events, in order to measure or predict risk. One risk metric, the superquantile, possesses several properties that make it ...