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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1148,
author = {Manuel L. Esqu\'\i vel and Lu\'\i s Dimas and Jo\~ao Tiago Mexia and Philippe Didier},
title = {Small perturbations with large effects on value-at-risk},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {33},
year = {2013},
pages = {151-169},
zbl = {1315.60021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1148}
}
Manuel L. Esquível; Luís Dimas; João Tiago Mexia; Philippe Didier. Small perturbations with large effects on value-at-risk. Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) pp. 151-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1148/
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