A note on the Galambos copula and its associated Bernstein function

• Autorzy: Jan-Frederik Mai
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Galambos copula; Bernstein function; min-stable multivariate exponential distribution; strong IDT process; infinite divisibility

Kategorie tematyczne

• 62H05: Characterization and structure theory
• 62H20: Measures of association (correlation, canonical correlation, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2013-12-04

zaakceptowano

2014-02-19

online

2014-03-20

Twórcy

autor

Jan-Frederik Mai

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

Bibliografia

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• [15] J.-F. Mai, M. Scherer, Characterization of extendible distributions with exponential minima via stochastic processes that are infinitely divisible with respect to time, Extremes, in press, DOI 10.1007/s10687-013-0175-4 (2013). [Crossref]
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Identyfikatory

DOI

10.2478/demo-2014-0002