Parameter estimation of a bivariate compound Poisson process

Habib Esmaeili, Claudia Klüppelberg

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivariate compound Poisson processes. A simulation study investigates the small sample behaviour of the MLEs, where we also suggest a new simulation algorithm. Finally, we apply our method to Danish fire insurance data.

Original languageEnglish
Pages (from-to)224-233
Number of pages10
JournalInsurance: Mathematics and Economics
Issue number2
StatePublished - Oct 2010


  • Dependence modelling
  • Lévy copula
  • Lévy measure
  • Lévy process
  • Maximum likelihood estimation
  • Multivariate compound Poisson process


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