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Properties of the induced semigroup of an Archimedean copula

Włodzimierz Wysocki (2004)

Applicationes Mathematicae

It is shown that to every Archimedean copula H there corresponds a one-parameter semigroup of transformations of the interval [0,1]. If the elements of the semigroup are diffeomorphisms, then it determines a special function v H called the vector generator. Its knowledge permits finding a pseudoinverse y = h(x) of the additive generator of the Archimedean copula H by solving the differential equation d y / d x = v H ( y ) / x with initial condition ( d h / d x ) ( 0 ) = - 1 . Weak convergence of Archimedean copulas is characterized in terms of vector...

Quantile of a Mixture with Application to Model Risk Assessment

Carole Bernard, Steven Vanduffel (2015)

Dependence Modeling

We provide an explicit expression for the quantile of a mixture of two random variables. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial dependence information is available. This paper complements the work of [4].

Quasi-copulas with quadratic sections in one variable

José Antonio Rodríguez–Lallena, Manuel Úbeda-Flores (2008)

Kybernetika

We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.

Random noise and perturbation of copulas

Radko Mesiar, Ayyub Sheikhi, Magda Komorníková (2019)

Kybernetika

For a random vector ( X , Y ) characterized by a copula C X , Y we study its perturbation C X + Z , Y characterizing the random vector ( X + Z , Y ) affected by a noise Z independent of both X and Y . Several examples are added, including a new comprehensive parametric copula family 𝒞 k k ∈ [ - ∞ , ∞ ] .

Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante, Erich Peter Klement, José Quesada-Molina, Peter Sarkoci (2007)

Kybernetika

We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

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