Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models

Lluís Bermúdez, Dimitris Karlis and Isabel Morillo
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Lluís Bermúdez: Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Diagonal 690, 08034 Barcelona, Spain
Dimitris Karlis: Department of Statistics, Athens University of Economics and Business, 10434 Athens, Greece
Isabel Morillo: Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Diagonal 690, 08034 Barcelona, Spain

Risks, 2020, vol. 8, issue 1, 1-13

Abstract: When modelling insurance claim count data, the actuary often observes overdispersion and an excess of zeros that may be caused by unobserved heterogeneity. A common approach to accounting for overdispersion is to consider models with some overdispersed distribution as opposed to Poisson models. Zero-inflated, hurdle and compound frequency models are typically applied to insurance data to account for such a feature of the data. However, a natural way to deal with unobserved heterogeneity is to consider mixtures of a simpler models. In this paper, we consider k -finite mixtures of some typical regression models. This approach has interesting features: first, it allows for overdispersion and the zero-inflated model represents a special case, and second, it allows for an elegant interpretation based on the typical clustering application of finite mixture models. k -finite mixture models are applied to a car insurance claim dataset in order to analyse whether the problem of unobserved heterogeneity requires a richer structure for risk classification. Our results show that the data consist of two subpopulations for which the regression structure is different.

Keywords: zero-inflation; overdispersion; automobile insurance; risk classification; risk selection (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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