Displaying similar documents to “On uniform tail expansions of multivariate copulas and wide convergence of measures”

On uniform tail expansions of bivariate copulas

Piotr Jaworski (2004)

Applicationes Mathematicae

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The theory of copulas provides a useful tool for modelling dependence in risk management. The goal of this paper is to describe the tail behaviour of bivariate copulas and its role in modelling extreme events. We say that a bivariate copula has a uniform lower tail expansion if near the origin it can be approximated by a homogeneous function L(u,v) of degree 1; and it is said to have a uniform upper tail expansion if the associated survival copula has a lower tail expansion. In this...

Constructing copulas by means of pairs of order statistics

Ali Dolati, Manuel Úbeda-Flores (2009)

Kybernetika

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In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.

Copula–Induced Measures of Concordance

Sebastian Fuchs (2016)

Dependence Modeling

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We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas....

Characterizations of bivariate conic, extreme value, and Archimax copulas

Susanne Saminger-Platz, José De Jesús Arias-García, Radko Mesiar, Erich Peter Klement (2017)

Dependence Modeling

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Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively.

Bounds on integrals with respect to multivariate copulas

Michael Preischl (2016)

Dependence Modeling

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In this paper, we present a method to obtain upper and lower bounds on integrals with respect to copulas by solving the corresponding assignment problems (AP’s). In their 2014 paper, Hofer and Iacó proposed this approach for two dimensions and stated the generalization to arbitrary dimensons as an open problem. We will clarify the connection between copulas and AP’s and thus find an extension to the multidimensional case. Furthermore, we provide convergence statements and, as applications,...

Invariant copulas

Erich Peter Klement, Radko Mesiar, Endre Pap (2002)

Kybernetika

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A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

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We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally,...

My introduction to copulas

Fabrizio Durante, Giovanni Puccetti, Matthias Scherer, Steven Vanduffel (2017)

Dependence Modeling

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