Tid: 11 maj 2009 kl 15.15-17.00

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Alexander J. McNeil, Heriot-Watt University, Edinburgh

Titel: From Archimedean to Liouville Copulas

Abstract

The Archimedean copula family is used in a number of actuarial and financial applications including: the construction of multivariate loss distributions; frailty models for dependent lifetimes; models for dependent defaults in credit risk. We show how the Archimedean copulas are most usefully viewed as the survival copulas of so-called simplex distributions, which are scale mixtures of uniform distributions on simplices. This representation allows us to construct a rich variety of new Archimedean copulas in different dimensions and to solve in principle the problem of generating samples from any Archimedean copula. It also sheds light on the dependence properties of Archimedean copulas and their relationship to the mixing or so-called radial distribution of the simplex distribution.

Armed with these insights we generalise the Archimedean copulas to the Liouville copulas, which are the survival copulas of Liouville distributions, these being scale mixtures of Dirichlet distributions. This generalisation yields asymmetric, non-exchangeable copulas, whose properties can again be understood in terms of the mixing or radial distribution of the Liouville distribution.

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