A Posteriori Ratemaking With Panel Data

Boucher, Jean‐Philippe; Inoussa, Rofick

doi:10.1017/asb.2014.11

Cited by 33 publications

(43 citation statements)

References 15 publications

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“…Policyholders staying in the sample drive about 0.2 km more per day. Boucher and Inoussa (2014) describe three types of models for longitudinal data. As Boucher et al (2008) suggest that the conditional model performs poorly in fitting, we run two alternatives, the random effect model and the marginal model.…”

Section: Robustness Of Results and Model Selectionmentioning

confidence: 99%

The Use of Annual Mileage as a Rating Variable

2015

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Auto insurance companies are at a crossroads. Several variables commonly used, such as gender and territory, are being questioned by regulators. Insurers are being pressured to find new variables that predict accidents more accurately and are socially acceptable. Annual mileage seems an ideal candidate. The recent development of GPS systems, on-board computers, and telematics devices, and the rapid decrease in price of the new technologies, should induce carriers to explore ways to introduce Pay-As -You-Drive insurance. We use the unique database of a major insur er in Taiwan to investigate whether annual mileage should be introduced as a rating variable in third-party liability insurance. We find that annual mileage is an extremely powerful predictor of the number of claims at-fault. Its significance, as measured by Wald's chi -square and its associated p-value, by far exceed that of all other variables, including bonus-malus. This conclusion applies independently of all other variables possibly included in rating. The inclusion of mileage as a new variable should, however, not take place at the expense of bonus-malus systems; rather the information contained in the bonus-malus premium level complements the value of annual mileage. An accurate rating system should therefore include annual mileage and bonus-malus as the two main building blocks, possibly supplemented by the use of other variables like age, territory, and engine cubic capacity. While Taiwan has specific characteristics (high traffic density, mild bonus-malus system, limited compulsory auto coverage), our results are so strong that we can confidently conjecture that they extend to all affluent countries. Auto insurance companies are at a crossroads. Several variables commonly used, such as gender and territory, are being questioned by regulators. Insurers are being pressured to find new variables that predict accidents more accurately and are socially acceptable. Annual mileage seems an ideal candidate. The recent development of GPS systems, on-board computers, and telematics devices, and the rapid decrease in price of the new technologies, should induce carriers to explore ways to introduce Pay-As-You-Drive insurance.We use the unique database of a major insurer in Taiwan to investigate whether annual mileage should be introduced as a rating variable in third-party liability insurance. We find that annual mileage is an extremely powerful predictor of the number of claims at-fault. Its significance, as measured by Wald's chi-square and its associated p-value, by far exceed that of all other variables, including bonusmalus. This conclusion applies independently of all other variables possibly included in rating. The inclusion of mileage as a new variable should, however, not take place at the expense of bonus-malus systems; rather the information contained in the bonus-malus premium level complements the value of annual mileage. An accurate rating system should therefore include annual mileage and bonus-malus as the two main building blocks...

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Section: Robustness Of Results and Model Selectionmentioning

confidence: 99%

The Use of Annual Mileage as a Rating Variable

2015

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“…However, in Canada, nonat-fault claims correspond to specific type of accidents, more related to the car's location in the accident. This is well known in Canada, and even if insurers cannot increase the premium for non-at-fault claims, insurers must sometimes find original ways to penalize drivers with non-at-fault claims (see Boucher and Inoussa (2014)). Consequently, for possibly the same reasons cited above for collision and comprehensive coverages that might lead to dependence, it seems logical to believe that dependence can exist between these two types of collision claims as well.…”

Section: Data Usedmentioning

confidence: 99%

“…For example, Pinquet (1998) uses Poisson residuals to create dependence between at-fault and not-at-fault claims in automobile insurance, while Boucher and Inoussa (2014) use Bonus-Malus Systems with specific penalty rules allowing different claim types to affect the premium. Frees and Valdez (2008) also model various type of claims by decomposing all possibilities of claim types that may occur for a single accident.…”

Section: Introductionmentioning

confidence: 99%

Sarmanov family of multivariate distributions for bivariate dynamic claim counts model

Abdallah

Boucher²,

Cossette

2016

Insurance: Mathematics and Economics

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To predict future claims, it is well-known that the most recent claims are more predictive than older ones. However, classic panel data models for claim counts, such as the multivariate negative binomial distribution, do not put any time weight on past claims. More complex models can be used to consider this property, but often need numerical procedures to estimate parameters. When we want to add a dependence between different claim count types, the task would be even more difficult to handle. In this paper, we propose a bivariate dynamic model for claim counts, where past claims experience of a given claim type is used to better predict the other type of claims. This new bivariate dynamic distribution for claim counts is based on random effects that come from the Sarmanov family of multivariate distributions. To obtain a proper dynamic distribution based on this kind of bivariate priors, an approximation of the posterior distribution of the random effects is proposed. The resulting model can be seen as an extension of the dynamic heterogeneity model described in Bolancé et al. (2007). We apply this model to two samples of data from a major Canadian insurance company, where we show that the proposed model is one of the best models to adjust the data. We also show that the proposed model allows more flexibility in computing predictive premiums because closed-form expressions can be easily derived for the predictive distribution, the moments and the predictive moments.

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“…Insurers tended to focus on the risk associated with the policy contracted during a certain period, typically one year in non-life lines. Indeed, various studies adopt this approach when dealing with pricing in auto insurance lines (see, for example, Abdallah et al, 2016;Boucher and Inoussa, 2014;Boucher et al, 2007;Bolancé et al, 2003;Pinquet et al, 2001). However, few papers to date have attempted to analyse the policyholder's accident risk from a multivariate perspective.…”

Section: Introductionmentioning

confidence: 99%

Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Bolancé

Vernic

2019

Insurance: Mathematics and Economics

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Institute of Applied Economics (IREA) in Barcelona was founded in 2005, as a research institute in applied economics. Three consolidated research groups make up the institute: AQR, RISK and GiM, and a large number of members are involved in the Institute. IREA focuses on four priority lines of investigation: (i) the quantitative study of regional and urban economic activity and analysis of regional and local economic policies, (ii) study of public economic activity in markets, particularly in the fields of empirical evaluation of privatization, the regulation and competition in the markets of public services using state of industrial economy, (iii) risk analysis in finance and insurance, and (iv) the development of micro and macro econometrics applied for the analysis of economic activity, particularly for quantitative evaluation of public policies. IREA Working Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. For that reason, IREA Working Papers may not be reproduced or distributed without the written consent of the author. A revised version may be available directly from the author. Any opinions expressed here are those of the author(s) and not those of IREA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions.

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A Posteriori Ratemaking With Panel Data

Cited by 33 publications

References 15 publications

The Use of Annual Mileage as a Rating Variable

The Use of Annual Mileage as a Rating Variable

Sarmanov family of multivariate distributions for bivariate dynamic claim counts model

Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

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