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A note on the Galambos copula and its associated Bernstein function

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  • Mai Jan-Frederik

    (Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, 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.

Suggested Citation

  • Mai Jan-Frederik, 2014. "A note on the Galambos copula and its associated Bernstein function," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, March.
    • Handle: RePEc:vrs:demode:v:2:y:2014:i:1:p:8:n:2
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    References listed on IDEAS

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    1. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    2. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    3. Es-sebaiy, Khalifa & Ouknine, Youssef, 2008. "How rich is the class of processes which are infinitely divisible with respect to time?," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 537-547, April.
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