European Actuarial Journal

, Volume 3, Issue 1, pp 273–294

On the analysis of a class of loss models incorporating time dependence

Original Research Paper


A model for the number or amount of aggregate claim values on a portfolio of insurance business is analysed. The number of claims process is assumed to be a (possibly time transformed) mixed Poisson process, and the value of a claim is allowed to depend on the time of incurral as well as the end point of the observation period. The mixed Erlang assumption for claim amounts is seen to carry over to the aggregate claims fairly generally. Special cases of the model include the usual aggregate claims model with or without inflation, as well as a model for the incurred but not reported claims (IBNR), also with or without inflation. Connections between the inflation and IBNR models are established, and the notions of self-decomposability and discrete self-decomposability are seen to be relevant. Various examples are presented illustrating the ideas, and a numerical example is considered demonstrating how Panjer-type recursions may be employed to evaluate distributions of interest.


Compound distribution Mixed Poisson Mixed Erlang Gamma distribution Order statistic property Inflation Incurred but not reported Self-decomposable Discrete self-decomposable Infinite server MX/M/∞ queue 


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Copyright information

© DAV / DGVFM 2013

Authors and Affiliations

  • Ling Guo
    • 1
  • David Landriault
    • 1
  • Gordon E. Willmot
    • 1
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

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