On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

German Bernhart; Jan-Frederik Mai; Matthias Scherer

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 29-46, electronic only
  • ISSN: 2300-2298

Abstract

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Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

How to cite

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German Bernhart, Jan-Frederik Mai, and Matthias Scherer. "On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions." Dependence Modeling 3.1 (2015): 29-46, electronic only. <http://eudml.org/doc/271008>.

@article{GermanBernhart2015,
abstract = {Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.},
author = {German Bernhart, Jan-Frederik Mai, Matthias Scherer},
journal = {Dependence Modeling},
keywords = {MSMVE distributions; Bernstein functions; IDT-frailty copulas; IDT processes; extreme-value copulas},
language = {eng},
number = {1},
pages = {29-46, electronic only},
title = {On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions},
url = {http://eudml.org/doc/271008},
volume = {3},
year = {2015},
}

TY - JOUR
AU - German Bernhart
AU - Jan-Frederik Mai
AU - Matthias Scherer
TI - On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 29
EP - 46, electronic only
AB - Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.
LA - eng
KW - MSMVE distributions; Bernstein functions; IDT-frailty copulas; IDT processes; extreme-value copulas
UR - http://eudml.org/doc/271008
ER -

References

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