Small perturbations with large effects on value-at-risk

Manuel L. Esquível; Luís Dimas; João Tiago Mexia; Philippe Didier

Discussiones Mathematicae Probability and Statistics (2013)

  • Volume: 33, Issue: 1-2, page 151-169
  • ISSN: 1509-9423

Abstract

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We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.

How to cite

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Manuel L. Esquível, et al. "Small perturbations with large effects on value-at-risk." Discussiones Mathematicae Probability and Statistics 33.1-2 (2013): 151-169. <http://eudml.org/doc/271056>.

@article{ManuelL2013,
abstract = {We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.},
author = {Manuel L. Esquível, Luís Dimas, João Tiago Mexia, Philippe Didier},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Gaussian perturbation; value-at-risk; delta-normal model},
language = {eng},
number = {1-2},
pages = {151-169},
title = {Small perturbations with large effects on value-at-risk},
url = {http://eudml.org/doc/271056},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Manuel L. Esquível
AU - Luís Dimas
AU - João Tiago Mexia
AU - Philippe Didier
TI - Small perturbations with large effects on value-at-risk
JO - Discussiones Mathematicae Probability and Statistics
PY - 2013
VL - 33
IS - 1-2
SP - 151
EP - 169
AB - We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.
LA - eng
KW - Gaussian perturbation; value-at-risk; delta-normal model
UR - http://eudml.org/doc/271056
ER -

References

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