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Multivariate Counting Processes: Copulas and Beyond

Published online by Cambridge University Press:  17 April 2015

Nicole Bäuerle  and
Rudolf Grübel
Nicole Bäuerle
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, E-mail: [email protected], [email protected]
Rudolf Grübel
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, E-mail: [email protected], [email protected]
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Abstract

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Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the events of a background Poisson process with constant intensity are moved forward in time by a random amount and possibly deleted; here we think of the events of the background process as triggering later claims in different categories. We discuss structural aspects of these models, their dependence properties together with stochastic order aspects, and also some related computational issues. Various actuarial applications are indicated.

Keywords

Claim arrival processesdependencypoint processesPoisson processesstochastic modellingstochastic ordering
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 2 , November 2005 , pp. 379 - 408
Copyright
Copyright © ASTIN Bulletin 2005

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