On the Tail Behavior of Sums of Dependent Risks

Barbe, Philippe; Fougères, Anne-Laure; Genest, Christian

doi:10.2143/ast.36.2.2017926

Cited by 53 publications

(63 citation statements)

References 16 publications

(48 reference statements)

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“…Alink et al (2004Alink et al ( , 2005 and Wüthrich (2003) also obtained similar results for Gumbel or Weibull extreme-value families. Using the results by de Haan and Resnick (1977), Barbe et al (2006) extend (6) beyond Archimedean dependence structures, where X i is multivariate regularly varying (for definition see Barbe et al 2006). For Archimedean dependence structure their result agrees with (6).…”

supporting

confidence: 55%

Archimedean copulas with applications to $${{\mathrm{VaR}}}$$ VaR estimation

Furmańczyk

2015

Stat Methods Appl

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Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics. We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR estimation for sums of data from Archimedean copulas.

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supporting

confidence: 55%

Archimedean copulas with applications to $${{\mathrm{VaR}}}$$ VaR estimation

Furmańczyk

2015

Stat Methods Appl

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“…Consequently, Theorem 7.48 of [26] implies thatC ∈ M(C Ga 1/α ), as claimed. Example 1 justifies attaching the name of Galambos to the family of multivariate extreme value copulas C Ga θ , which also appears in [2]. …”

Section: Proposition 3 Let C Be An Archimedean Copula With Radial Partmentioning

confidence: 99%

Extremal behavior of Archimedean copulas

Larsson

Nešlehová

2011

Adv. Appl. Probab.

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We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an 1 -symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

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“…For recent references on this topic, we refer the reader to Alink et al (2004), Barbe et al (2006), and Kortschak and Albrecher (2008), among others. They all used multivariate copula functions to model the underlying dependence structures.…”

Section: The Multivariate Casementioning

confidence: 99%