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A note on the Galambos copula and its associated Bernstein function

100%

Mai J.-F.

Dependence Modeling

2014

tom 2

nr 1

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.

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

51%

Bernhart G., Mai J.-F., Scherer M.

Dependence Modeling

2015

tom 3

nr 1

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

Ograniczanie wyników

2 Dependence Modeling

2 Mai J.-F.

1 Bernhart G.

1 Scherer M.

1 2015

1 2014

Wyniki wyszukiwania

A note on the Galambos copula and its associated Bernstein function

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions