Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models

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.

Machine Learning in Forecasting Motor Insurance Claims

“…Qazvini (2019) employs ML methods to predict the number of zero claims (i.e., claims that have not been reported) based on telematics data (on French motor third party liability). Bermúdez et al (2020) apply ML approaches to model insurance claim counts with an emphasis on the overdispersion and the excess number of zero claims, which may be the outcome of unobserved heterogeneity. Bärtl and Krummaker (2020) attempt to predict the occurrence and the magnitude of export credit insurance claims with the use of ML techniques.…”

A Study of Generalized Linear Mixed Model for Count Data Using Hierarchical Bayes Method

“…Let 𝑦 𝑖𝑗 is the count taken from the j-th observation and the i-th cluster which are independent of each other. (Berliana et al, 2019;Bermúdez et al, 2020;Mallya et al, 2018).…”

A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

“…It should be noted that the popularity of mixture models has spread substantially in works of applied and methodological interest across various disciplines such as insurance, economics, finance, biology, genetics, medicine, and most recently in the sphere of artificial intelligence. A few notable works across the aforementioned disciplines include these of Titterington (1990), Samadani (1995), Yung (1997), Allison et al (2002), Karlis and Xekalaki (2005) Bermúdez et al (2020), though this list is certainly not exhaustive. A short summary of the main characteristics of the class of finite mixture models with component distributions stemming from different parametric families, which we consider in this study follows.…”