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Multivariate Counting Processes: Copulas and Beyond

  • Nicole Bäuerle (a1) and Rudolf Grübel (a1)
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T.C. Christofides and E.A. Vaggelatou (2004) Connection between supermodular ordering and positive/negative association. Journal of Multivariate Analysis, 88, 138151.

J.D. Esary , F. Proschan and D.W. Walkup (1967) Association of random variables with applications. Ann. Math. Stat., 38, 14661474.

H. Joe (1997) Multivariate Models and Dependence Concepts. Chapman and Hall, London.

F. Lindskog and A.J. Mcneil (2003) Common Poisson shock models: applications to insurance and credit risk modelling. ASTIN Bulletin, 33, 209238.

R.B. Nelsen (1999) An Introduction to Copulas. Lecture Notes in Statistics 139. Springer, New York.

D. Pfeifer and J. Neslehova (2004) Modeling and generating dependent risk processes for IRM and DFA. ASTIN Bulletin, 34, 333360.

S.I. Resnick (1987) Extreme Values, Regular Variation and Point Processes. Springer, New York.

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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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