Modelling the aggregate loss for insurance claims with dependence

Ning Wang, Linyi Qian, Nan Zhang, Zehui Liu

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a new model to relax the impractical independence assumption between the counts and the amounts of insurance claims, which is commonly made in the existing literature for mathematical convenience. When considering the dependence between the claim counts and the claim amounts, we treat the number of claims as an explanatory variable in the model for claim sizes. Besides, generalized linear models (GLMs) are employed to fit the claim counts in a given time period. To describe the claim amounts which are repeatedly measured on a group of subjects over time, we adopt generalized linear mixed models (GLMMs) to incorporate the dependence among the related observations on the same subject. In addition, a Monte Carlo Expectation-Maximization (MCEM) algorithm is proposed by using a Metropolis-Hastings algorithm sampling scheme to obtain the maximum likelihood estimates of the parameters for the linear predictor and variance component. Finally, we conduct a simulation to illustrate the feasibility of our proposed model.
Original languageEnglish
Pages (from-to)2080-2095
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Issue number9
Early online date2 Sept 2019
Publication statusPublished - 3 May 2021


  • claim amounts
  • Claim counts
  • dependence
  • generalized linear mixed models
  • generalized linear models
  • MCEM algorithm
  • Metropolis-Hastings algorithm


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