Displaying similar documents to “Proving the characterization of Archimedean copulas via Dini derivatives”

Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas

J. Górecki, M. Hofert, M. Holeňa (2017)

Dependence Modeling

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Several successful approaches to structure determination of hierarchical Archimedean copulas (HACs) proposed in the literature rely on agglomerative clustering and Kendall’s correlation coefficient. However, there has not been presented any theoretical proof justifying such approaches. This work fills this gap and introduces a theorem showing that, given the matrix of the pairwise Kendall correlation coefficients corresponding to a HAC, its structure can be recovered by an agglomerative...

On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

Elena Di Bernardino, Didier Rullière (2016)

Dependence Modeling

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An important topic in Quantitative Risk Management concerns the modeling of dependence among risk sources and in this regard Archimedean copulas appear to be very useful. However, they exhibit symmetry, which is not always consistent with patterns observed in real world data. We investigate extensions of the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based on the observation that when applied to the copula the inverse function of the generator...

Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

Marcin Dudziński, Konrad Furmańczyk (2017)

Open Mathematics

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Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.

A remark on associative copulas

Piotr Mikusiński, Michael D. Taylor (1999)

Commentationes Mathematicae Universitatis Carolinae

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A method for producing associative copulas from a binary operation and a convex function on an interval is described.

Dynamic dependence ordering for Archimedean copulas and distorted copulas

Arthur Charpentier (2008)

Kybernetika

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This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i. e. given remaining lifetimes X , to compare the dependence of X given X > t , and X given X > s , where s > t . More precisely, analytical results will be obtained in the case the survival copula of X is either Archimedean or a distorted copula. The case of a frailty based model will also be discussed in details.

My introduction to copulas

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

Dependence Modeling

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A copula test space model how to avoid the wrong copula choice

Frederik Michiels, Ann De Schepper (2008)

Kybernetika

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We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP...

Univariate conditioning of copulas

Radko Mesiar, Vladimír Jágr, Monika Juráňová, Magda Komorníková (2008)

Kybernetika

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The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula...

A two-component copula with links to insurance

S. Ismail, G. Yu, G. Reinert, T. Maynard (2017)

Dependence Modeling

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This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit...