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Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems

TL;DR: In this article, the authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information, and summarise the relationship between experience rating systems and risk classification.
Abstract: There are a wide range of variables for actuaries to consider when calculating a motorist’s insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists’ rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information.
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Journal ArticleDOI
01 Jun 2017
TL;DR: This study proves that including standard telematics variables significantly improves the risk assessment of customers, and suggests that if a manager wants to implement Usage-Based-Insurances, Pay-As-You-Drive related variables are most valuable to tailor the premium to the risk.
Abstract: The advent of the Internet of Things enables companies to collect an increasing amount of sensor generated data which creates plenty of new business opportunities. This study investigates how this sensor data can improve the risk selection process in an insurance company. More specifically, several risk assessment models based on three different data mining techniques are augmented with driving behaviour data collected from In-Vehicle Data Recorders. This study proves that including standard telematics variables significantly improves the risk assessment of customers. As a result, insurers will be better able to tailor their products to the customers' risk profile. Moreover, this research illustrates the importance of including industry knowledge, combined with data expertise, in the variable creation process. Especially when a regulator forces the use of easily interpretable data mining techniques, expert-based telematics variables are able to improve the risk assessment model in addition to the standard telematics variables. Further, the results suggest that if a manager wants to implement Usage-Based-Insurances, Pay-As-You-Drive related variables are most valuable to tailor the premium to the risk. Finally, the study illustrates that this new type of telematics-based insurance product can quickly be implemented since three months of data is already sufficient to obtain the best risk estimations. This study proves the value of telematics-based data in the risk selection process of an insurance companyIt compares the performance of three models in this context: a logistic regression, random forests and artificial neural networks modelThis research illustrates the importance of industry knowledge in the variable creation processThree months of data is sufficient to obtain the best risk estimations

100 citations


Cites methods from "Actuarial Modelling of Claim Counts..."

  • ...In the insurance industry, a generalized linear model with poisson distribution is often used to predict the claim counts [14]....

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Journal ArticleDOI
TL;DR: In this paper, the authors assume that the number of accidents is based on a Poisson distribution but that the claims is generated by censorship of this distribution, and then they present new models for panel count data based on the zero-inflated poisson distribution.
Abstract: P>The hunger for bonus is a well-known phenomenon in insurance, meaning that the insured does not report all of his accidents to save bonus on his next year's premium. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is generated by censorship of this Poisson distribution. Then, we present new models for panel count data based on the zero-inflated Poisson distribution. From the claims distributions, we propose an approximation of the accident distribution, which can provide insight into the behavior of insureds. A numerical illustration based on the reported claims of a Spanish insurance company is included to support this discussion.

89 citations


Cites background from "Actuarial Modelling of Claim Counts..."

  • ...Denuit et al. (2007) provides an exhaustive overview of count data models for insurance claims....

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Journal ArticleDOI
TL;DR: In this paper, a 2-finite mixture of bivariate Poisson regression models is proposed to model the overdispersion in the data, and it is shown that a simple zero-inflated bivariate poisson model does not suffice.
Abstract: In a recent paper Bermudez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models 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, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermudez [2009] and it is shown that the modelling of the data set can be improved considerably.

83 citations


Cites background or methods from "Actuarial Modelling of Claim Counts..."

  • ...In the univariate case, Lambert [1992] introduced the zero-inflated Poisson regression model....

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  • ...In the univariate case, Lambert [1992] introduced the zero-inflated Poisson regression model. Since then, there has been a considerable increase in the number of applications of zero-inflated regression models based on several different distributions. A comprehensive discussion of these applications can be found in Winkelmann [2008] and a specific application to insurance ratemaking is addressed in Boucher et al....

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Journal ArticleDOI
TL;DR: In this article, generalized additive models for location, scale and shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed.
Abstract: Generalized additive models for location, scale and, shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed. This approach allows the actuary to include risk factors not only in the mean but also in other key parameters governing the claiming behavior, like the degree of residual heterogeneity or the no-claim probability. In this broader setting, the Negative Binomial regression with cell-specific heterogeneity and the zero-inflated Poisson regression with cell-specific additional probability mass at zero are applied to model claim frequencies. New models for claim severities that can be applied either per claim or aggregated per year are also presented. Bayesian inference is based on efficient Markov chain Monte Carlo simulation techniques and allows for the simultaneous estimation of linear effects as well as of possible nonlinear effects, spatial variations and interactions between risk factors within the data set. To illustrate the relevance of this approach, a detailed case study is proposed based on the Belgian motor insurance portfolio studied in Denuit and Lang (2004).

68 citations

01 Jan 2016

63 citations


Cites background from "Actuarial Modelling of Claim Counts..."

  • ...The current state of the art (see Denuit et al. (2007) and de Jong and Heller (2008) for an overview) uses generalized linear models (GLMs) (McCullagh and Nelder, 1989), with typically a Poisson GLM for the claim counts and a gamma GLM for the claim severities....

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  • ...From a theoretical point of view, this can be motivated by the probabilistic framework of Poisson processes (Denuit et al., 2007)....

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  • ...Despite the deregulation, many insurers in the Belgian market still apply the former mandatory system (Denuit et al., 2007)....

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  • ...This phenomenon is known as the hunger for bonus (Denuit et al., 2007)....

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