[hal-00996440] Bregman superquantiles Estimation methods and applications

In this work we extend some quantities introduced in Optimization of conditional value-at-risk of RT 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 RT Rockafellar are studied in the case of Bregman superquantile Furthermore we deal with asymptotic properties of a Monte Carlo estimator of the Bregman superquantile



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