A note on the Galambos copula and its associated Bernstein function

Mai Jan-Frederik
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Mai Jan-Frederik: Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany

Dependence Modeling, 2014, vol. 2, issue 1, 8

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.

Keywords: Galambos copula; Bernstein function; min-stable multivariate exponential distribution; strong IDT process; infinite divisibility; 62H20; 62H05; Galambos copula; Bernstein function; min-stable multivariate exponential distribution; strong IDT process; infinite divisibility; 62H20; 62H05 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:2:y:2014:i:1:p:8:n:2

DOI: 10.2478/demo-2014-0002

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