Bregman superquantiles. Estimation methods and applications
Statistics Theory
2016-01-07 v4 Risk Management
Statistics Theory
Abstract
In this work, we extend some quantities introduced in "Optimization of conditional value-at-risk" of R.T Rockafellar and S. Uryasev to the case where the proximity between real numbers is measured by using a Bregman divergence. This leads to the definition of the Bregman superquantile. Axioms of a coherent measure of risk discussed in "Coherent approches to risk in optimization under uncertainty" of R.T Rockafellar are studied in the case of Bregman superquantile. Furthermore, we deal with asymptotic properties of a Monte Carlo estimator of the Bregman superquantile.
Cite
@article{arxiv.1405.6677,
title = {Bregman superquantiles. Estimation methods and applications},
author = {Tatiana Labopin-Richard and Fabrice Gamboa and Aurélien Garivier and Bertrand Iooss},
journal= {arXiv preprint arXiv:1405.6677},
year = {2016}
}