On the link between credibility and frequency premium

Bolancé, Catalina; Guillén, Montserrat; Pinquet, Jean

doi:10.1016/j.insmatheco.2008.05.015

Cited by 10 publications

(9 citation statements)

References 15 publications

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“…For each policy, the information at the beginning of the period and the total number of claims from policyholders "at fault" were reported for each year. The exogenous variables, described in Table 1 outline the covariates, and this data set have previously been used in Pinquet et al (2001), Brouhns et al (2003), Bolancé et al (2003), Bolancé et al (2008), Boucher et al (2007), Boucher and Denuit (2008) (2009). In this study, all customers had held a policy with the company for at least three years.…”

Section: The Datamentioning

confidence: 99%

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Bermúdez

Karlis

2012

Computational Statistics & Data Analysis

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Bivariate Poisson regression models for ratemaking in car insurance has been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, it is shown that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Finally, an EM algorithm is provided in order to ensure the models' ease-offit. These models are applied to an automobile insurance claims data set and it is shown that the modelling of the data set can be improved considerably.

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Section: The Datamentioning

confidence: 99%

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Bermúdez

Karlis

2012

Computational Statistics & Data Analysis

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“…The definition and some descriptive statistics of the variables are presented in Table 1. This dataset has previously been used in Pinquet et al (2001), Brouhns et al (2003), Bolancé et al (2003Bolancé et al ( , 2008, Boucher et al (2007Boucher et al ( , 2009, Boucher and Denuit (2008), Bermúdez (2009) and Bermúdez and Karlis (2012).…”

Section: Data Descriptionmentioning

confidence: 99%

Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models

Bermúdez

Karlis

Morillo

2020

Risks

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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.

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“…This results contradicts the theory of informational monopoly power. 5 3 Allowance for unobserved heterogeneity by random effects models…”

Section: Experience Rating Schemes and Cross-subsidies In The Non-lifmentioning

confidence: 99%

“…The model also includes an elasticity between the lapse rate and relative prices between the incumbent insurer and its competitors. 5 At the opposite, life and health insurance products are often front-loaded, and sometimes heavily without any surrender value as is the case for long-term care insurance. Hendel and Lizzeri (2003) provide an economic analysis of front-loading in term-life insurance in the US.…”

Section: Experience Rating Schemes and Cross-subsidies In The Non-lifmentioning

confidence: 99%

Experience Rating in Nonlife Insurance

Pinquet¹

2013

Handbook of Insurance

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Résumé:Cet article présente les modèles statistiques conduisant à la tarification a posteriori en assurance. Les corrélations entre variables de risque peuvent s'expliquer de manière endogène ou exogène. L'interprétation retenue par les modèles actuariels est exogène et reflète la contagion positive habituellement observée pour les nombres de sinistres. Cette contagion positive peut être expliquée par la révélation dans le temps de caractéristiques cachées des lois de risque. Ces caractéristiques sont représentées par des effets fixes qui sont prédits avec un modèle à effets aléatoires. Cet article aborde les problèmes d'identification de la nature de la dynamique des données d'assurance non-vie. Des exemples de prédiction sont donnés pour des modèles de comptage avec des effets aléatoires constants ou dynamiques, une ou plusieurs équations, et pour des modèles sur les nombres et les coûts d'évènements. Abstract:This paper presents statistical models which lead to experience rating in insurance. Serial correlation for risk variables can receive endogeneous or exogeneous explanations. The interpretation retained by actuarial models is exogeneous and reflects the positive contagion usually observed for the number of claims. This positive contagion can be explained by the revelation throughout time of a hidden features in the risk distributions. These features are represented by fixed effects which are predicted with a random effects model. This article discusses identification issues on the nature of the dynamics of non-life insurance data. Example of predictions are given for count data models with a constant or time-varying random effects, one or several equations, and for cost-number models on events.Classification :. C13, C14, C23, C25, C30. Mots clés :Effets fixes et aléatoires, surdispersion, principe de valeur espérée, crédibilité linéaire.

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On the link between credibility and frequency premium

Cited by 10 publications

References 15 publications

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models

Experience Rating in Nonlife Insurance

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