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arXiv · 1405.6677

Bregman superquantiles. Estimation methods and applications

Tatiana Labopin-Richard·Fabrice Gamboa·Aurélien Garivier·Bertrand Iooss
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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.

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Tatiana Labopin-Richard, Fabrice Gamboa, Aurélien Garivier, Bertrand Iooss. 2014-05-26. Bregman superquantiles. Estimation methods and applications. https://arxiv.org/abs/1405.6677

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