@article { ISI:000320487800008,
	title = {Simplified pair copula constructions: Limitations and extensions},
	journal = {Journal of Multivariate Analysis},
	volume = {119},
	year = {2013},
	month = {AUG},
	pages = {101-118},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {So-called pair copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model selection, the simplifying assumption, that copulas of conditional distributions do not depend on the values of the variables which they are conditioned on, is popular. We show that the only Archimedean copulas in dimension d >= 3 which are of the simplified type are those based on the Gamma Laplace transform or its extension, while the Student-t copulas are the only one arising from a scale mixture of Normals. Further, we illustrate how PCCs can be adapted for situations where conditional copulas depend on values which are conditioned on, and demonstrate a technique to assess the distance of a multivariate distribution from a nearby distribution that satisfies the simplifying assumption. (C) 2013 Published by Elsevier Inc.},
	keywords = {Archimedean copula, Conditional distribution, Elliptical copula, Pair copula construction},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2013.04.014},
	author = {Stoeber, Jakob and Joe, Harry and Czado, Claudia}
}
@article { ISI:000313478200008,
	title = {Tail comonotonicity and conservative risk measures},
	journal = {ASTIN Bulletin},
	volume = {42},
	number = {2},
	year = {2012},
	month = {NOV},
	pages = {601-629},
	publisher = {Peeters},
	type = {Article},
	abstract = {Tail comonotonicity, or asymptotic full dependence, is proposed as a reasonable conservative dependence structure for modeling dependent risks. Some sufficient conditions have been obtained to justify the conservativity of tail comonotonicity. Simulation studies also suggest that, by using tail comonotonicity, one does not lose too much accuracy but gain reasonable conservative risk measures, especially when considering high scenario risks. A copula model with tail comonotonicity is applied to an auto insurance dataset. Particular models for tail comonotonicity for loss data can be based on the BB2 and BB3 copula families and their multivariate extensions.},
	keywords = {Archimedean copula, asymptotic full dependence, conditional tail expectation, Copula, Dependence modeling, Laplace transform, regular variation},
	issn = {0515-0361},
	doi = {10.2143/AST42.2.2182810},
	author = {Hua, Lei and Joe, Harry}
}
@article { ISI:000309028900029,
	title = {Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures},
	journal = {Insurance Mathematics \& Economics},
	volume = {51},
	number = {2},
	year = {2012},
	month = {SEP},
	pages = {492-503},
	publisher = {Elsevier Science BV},
	type = {Article},
	abstract = {We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly varying tails, lead to a tail comonotonic dependence structure. For random variables that are in the maximum domain of attraction of either Frechet or Gumbel, we prove the asymptotic additivity property of Value at Risk and Conditional Tail Expectation. (C) 2012 Elsevier B.V. All rights reserved.},
	keywords = {Archimedean copula, asymptotic full dependence, Copula, Elliptical distributions, Extreme value distributions, Regularly varying, Slowly varying},
	issn = {0167-6687},
	doi = {10.1016/j.insmatheco.2012.07.006},
	author = {Hua, Lei and Joe, Harry}
}
@article { ISI:000293048300012,
	title = {Tail order and intermediate tail dependence of multivariate copulas},
	journal = {Journal of Multivariate Analysis},
	volume = {102},
	number = {10},
	year = {2011},
	month = {NOV},
	pages = {1454-1471},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {In order to study copula families that have tail patterns and tail asymmetry different from multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Archimedean copula, we relate the tail heaviness of a positive random variable to the tail behavior of the Archimedean copula constructed from the Laplace transform of the random variable, and extend the results of Charpentier and Segers [7] [A. Charpentier, J. Segers, Tails of multivariate Archimedean copulas, Journal of Multivariate Analysis 100 (7)(2009) 1521-1537] for upper tails of Archimedean copulas. In addition, a new one-parameter Archimedean copula family based on the Laplace transform of the inverse Gamma distribution is proposed; it possesses patterns of upper and lower tails not seen in commonly used copula families. Finally, tail orders are studied for copulas constructed from mixtures of max-infinitely divisible copulas. (C) 2011 Elsevier Inc. All rights reserved.},
	keywords = {Archimedean copula, Laplace transform, Max-infinitely divisible, Maximal moment, Reflection symmetry, regular variation, Tail asymmetry},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2011.05.011},
	author = {Hua, Lei and Joe, Harry}
}
