Compound Poisson approximations for individual models with dependent risks

This paper shows how compound Poisson distributions can be used to approximate the distribution of the total claim amount in the context of single- or multi-class individual risk models where dependence between the contracts arises through mixtures. Some of these models are generated by Archimedean copulas, and others are seen to fall under the purview of a general multi-class shock model whose structure is both intuitive and easily tractable. A numerical study is used to illustrate the quality of the approximation as a function of the heterogeneity and the dependence in the portfolio. A theoretical result is also provided which helps to explain the effect of dependence on the total claim amount when the contracts are linked through an Archimedean copula model.