Reference : Smoothed nonparametric maximum likelihood estimation of the risk distribution underly...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Smoothed nonparametric maximum likelihood estimation of the risk distribution underlying bonus-malus systems
Denuit, Michel [ > > ]
Lambert, Philippe mailto [Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales >]
Proceedings of the Casualty Actuarial Society
[en] Mixed Poisson distributions are widely used for modeling
claim counts when the portfolio is thought to be
heterogeneous. The risk (or mixing) distribution then
represents a measure of this heterogeneity. The aim of
this paper is to use a variant of the Patilea and Rolin
[15] smoothed version of the Simar [20] Non-Parametric
Maximum Likelihood Estimator of the risk distribution
in the mixed Poisson model. Empirical results based on
two data sets from automobile third-party liability insurance
demonstrate the relevance of this approach. The
design of merit-rating schemes is discussed in the second
part of the paper.

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