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Dependence Modeling

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A note on the Galambos copula and its associated Bernstein function

Jan-Frederik Mai
  • Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany
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Published Online: 2014-03-20 | DOI: https://doi.org/10.2478/demo-2014-0002

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

MSC: 62H20; 62H05

References

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About the article


Received: 2013-12-04

Accepted: 2014-02-19

Published Online: 2014-03-20


Citation Information: Dependence Modeling, Volume 2, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.2478/demo-2014-0002.

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© 2014 Jan-Frederik Mai. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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