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Blätter der DGVFM

, Volume 25, Issue 4, pp 781–793 | Cite as

On the stochastic increasingness of future claims in the Bühlmann linear credibility premium

  • Oana Purcaru
  • Michel Denuit
Article
  • 42 Downloads

Summary

Since Nelder & Verrall (1997), the connection between Generalized Linear Models (GLM’s) and credibility theory has been recognized in actuarial science. Specifically, the credibility construction amounts to add a random effect on the same scale as the fixed effects to model unexplained heterogeneity. The present paper aims to examine the dependence existing between future claims (severity or frequency components) and the Bühlmann linear credibility premium. As expected, future claims are shown to increase with the amount of Bühlmann premium.

Keywords

Probability Density Function Stochastic Dominance Predictive Distribution Linear Predictor Credibility Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Über die Zunahme zukünftiger Schadensfälle im linearen Bühlmann Kredibilitätspremium

Zusammenfassung

Seit Nelder & Verrall (1997) ist der Zusammenhang zwischen Verallgemeinerten Linearen Modellen (GLM’s) und Kredibilitätstheorie in den Aktuarwissenschaften allgemein bekannt. Insbesondere kann die Kredibilität durch Hinzunahme eines zufälligen Effekts mit gleicher Skala wie die fixen Effekte modelliert werden, um nicht-erklärte Heterogenität zu erfassen. Die vorliegende Arbeit befasst sich damit, Abhängigkeiten zwischen zukünftigen Schadensfällen (Schadenskostenoder Häufigkeiten) und der Bühlmannschen linearen Kredibilitätsprämie zu untersuchen. Wie erwartet nehmen zukünftige Schadensfälle mit der Höhe der Bühlmannprämie zu.

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Copyright information

© DAV/DGVFM 2002

Authors and Affiliations

  • Oana Purcaru
    • 1
  • Michel Denuit
    • 1
  1. 1.Louvain-la-Neuve

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