A note on the Galambos copula and its associated Bernstein function

Jan-Frederik Mai 1 , 2
  • 1 Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • 2 XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany

Abstract

There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some of its properties.

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Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.

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