Bregman superquantiles. Estimation methods and applications.

In this work, we extend some parameters built on a probability distribution introduced before 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 (that we can connect with several works in economy). Axioms of a coherent measure of risk discussed previously are studied in the case of Bregman superquantile. Furthermore, we deal with asymptotic properties of a Monte Carlo estimator of the Bregman superquantile. Several numerical tests confirm the theoretical results and an application illustrates the potential interests of the Bregman superquantile. ISSN (Online) 2300-2298, DOI: 10.1515/demo-2016-0004