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Multivariate counting processes: copulas and beyond

Bäuerle, Nicole; Grübel, Rudolf

Abstract:
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.


Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2005
Sprache Englisch
Identifikator DOI: 10.2143/AST.35.2.2003459
ISSN: 0515-0361
URN: urn:nbn:de:swb:90-436145
KITopen ID: 1000043614
Erschienen in Astin Bulletin
Band 35
Heft 2
Seiten 379-408
Schlagworte Claim arrival processes, dependency, point processes, Poisson processes, stochastic modelling, stochastic ordering
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