# Bregman superquantiles. Estimation methods and applications

T. Labopin-Richard; F. Gamboa; A. Garivier; B. Iooss

Dependence Modeling (2016)

- Volume: 4, Issue: 1, page 76-108, electronic only
- ISSN: 2300-2298

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topT. Labopin-Richard, et al. "Bregman superquantiles. Estimation methods and applications." Dependence Modeling 4.1 (2016): 76-108, electronic only. <http://eudml.org/doc/276435>.

@article{T2016,

abstract = {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 [18] or [9]). Axioms of a coherent measure of risk discussed previously (see [31] or [3]) 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.},

author = {T. Labopin-Richard, F. Gamboa, A. Garivier, B. Iooss},

journal = {Dependence Modeling},

keywords = {Coherent measure of risk; superquantile; Bregman superquantile; empirical estimation; asymptotic
behavior; coherent measure of risk; asymptotic behavior},

language = {eng},

number = {1},

pages = {76-108, electronic only},

title = {Bregman superquantiles. Estimation methods and applications},

url = {http://eudml.org/doc/276435},

volume = {4},

year = {2016},

}

TY - JOUR

AU - T. Labopin-Richard

AU - F. Gamboa

AU - A. Garivier

AU - B. Iooss

TI - Bregman superquantiles. Estimation methods and applications

JO - Dependence Modeling

PY - 2016

VL - 4

IS - 1

SP - 76

EP - 108, electronic only

AB - 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 [18] or [9]). Axioms of a coherent measure of risk discussed previously (see [31] or [3]) 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.

LA - eng

KW - Coherent measure of risk; superquantile; Bregman superquantile; empirical estimation; asymptotic
behavior; coherent measure of risk; asymptotic behavior

UR - http://eudml.org/doc/276435

ER -

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