In thiswork,we extend some parameters built on a probability distribution introduced before to the
casewhere the proximity between real numbers is measured by using a Bregman divergence. This leads to the
definition of the Bregman superquantile (thatwe can connect with severalworks in economy, see for example
 or ). Axioms of a coherent measure of risk discussed previously (see  or ) are studied in the case
of Bregman superquantile. Furthermore,we deal with asymptotic properties of aMonte Carlo estimator of the
Bregman superquantile. Several numerical tests confirm the theoretical results and an application illustrates
the potential interests of the Bregman superquantile.