Bayesian analysis of aggregate loss models Articles uri icon

publication date

  • January 2011

start page

  • 257

end page

  • 279

issue

  • 2

volume

  • 21

international standard serial number (ISSN)

  • 0960-1627

abstract

  • This paper describes a Bayesian approach to make inference for aggregate loss models in the insurance framework. A semiparametric model based on Coxian distributions is proposed for the approximation of both the interarrival time between claims and the claim size distributions. A Bayesian density estimation approach for the Coxian distribution is implemented using reversible jump Markov Chain Monte Carlo (MCMC) methods. The family of Coxian distributions is a very flexible mixture model that can capture the special features frequently observed in insurance claims. Furthermore, given the proposed Coxian approximation, it is possible to obtain closed expressions of the Laplace transforms of the total claim count and the total claim amount random variables. These properties allow us to obtain Bayesian estimations of the distributions of the number of claims and the total claim amount in a future time period, their main characteristics and credible intervals. The possibility of applying deductibles and maximum limits is also analyzed. The methodology is illustrated with a real data set provided by the insurance department of an international commercial company