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Duration dependence models for claim counts

  • Original Research Paper
  • Published:
Blätter der DGVFM

Abstract

The aim of the paper is to introduce new claim count distributions constructed from different waiting time assumptions, such as the Exponential, Gamma and Weibull distributions. These models are then fitted to panel data with Gamma distributed random effects. The random effects allow for serial dependence and take residual heterogeneity into account. Predictive distributions are obtained with the help of Markov Chain Monte Carlo simulations. The approach is illustrated on the basis of a Belgian motor third party liability insurance portfolio observed for three years.

Zusammenfassung

Der Artikel stellt neue Schadenzahlverteilungen vor, die aus verschiedenen Annahmen zur Wartezeitverteilung hergeleitet werden. Diese Modelle werden an Paneldaten mit gammaverteilten Zufallseffekten angepasst. Die zufälligen Effekte berücksichtigen serielle Abhängigkeit sowie Heterogenität der Differenzen. Durch Markov Chain Monte Carlo Simulationen werden Prognoseverteilungen gewonnen. Die Vorgehensweise wird anhand eines belgischen Kfz-Haftpflicht Bestandes, der über 3 Jahre beobachtet wird, illustriert.

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Authors and Affiliations

  1. Louvain-la-Neuve, Belgium

    Jean-Philippe Boucher & Michel Denuit

Authors
  1. Jean-Philippe Boucher
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  2. Michel Denuit
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Correspondence to Jean-Philippe Boucher.

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Boucher, JP., Denuit, M. Duration dependence models for claim counts . Blätter DGVFM 28, 29–45 (2007). https://doi.org/10.1007/s11857-007-0003-5

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  • DOI: https://doi.org/10.1007/s11857-007-0003-5

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