Designing Optimal Bonus-Malus Systems from Different Types of Claims

Pinquet, Jean

doi:10.2143/ast.28.2.519066

Cited by 52 publications

(44 citation statements)

References 6 publications

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“…For their data, Dionne and Vannasse established that a random e¤ects Poisson model provided a better …t than the usual Poisson and negative binomial models. Pinquet (1997Pinquet ( , 1998) extended this work, considering severity as well as frequency distributions. He also allowed for di¤erent lines of business, as well as an explicit correlation parameter between the frequency and the severity components.…”

Section: Frequency Componentmentioning

confidence: 99%

Hierarchical Insurance Claims Modeling

Frees

Valdez

2008

Journal of the American Statistical Association

165

117

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This work describes statistical modeling of detailed, micro-level automobile insurance records. We consider 1993-2001 data from a major insurance company in Singapore. By detailed micro-level records, we refer to experience at the individual vehicle level, including vehicle and driver characteristics, insurance coverage and claims experience, by year. The claims experience consists of detailed information on the type of insurance claim, such as whether the claim is due to injury to a third party, property damage to a third party or claims for damage to the insured, as well as the corresponding claim amount.We propose a hierarchical model for three components, corresponding to the frequency, type and severity of claims. The …rst is a negative binomial regression model for assessing claim frequency. The driver's gender, age, and no claims discount as well as vehicle age and type turn out to be important variables for predicting the event of a claim. The second is a multinomial logit model to predict the type of insurance claim, whether it is third party injury, third party property damage, insured's own damage or some combination. Year, vehicle age and vehicle type turn out to be important predictors for this component.Our third model is for the severity component. Here, we use a generalized beta of the second kind long-tailed distribution for claim amounts and also incorporate predictor variables. Year, vehicle age and a person's age turn out to be important predictors for this component. Not surprisingly, we show that there is a signi…cant dependence among the di¤erent claim types; we use a t-copula to account for this dependence.The three component model provides justi…cation for assessing the importance of a rating variable. When taken together, the integrated model allows an actuary to predict automobile claims more e¢ ciently than traditional methods. Using simulation, we demonstrate this by developing predictive distributions and calculating premiums under alternative reinsurance coverages.

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Section: Frequency Componentmentioning

confidence: 99%

Hierarchical Insurance Claims Modeling

Frees

Valdez

2008

Journal of the American Statistical Association

165

117

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“…Exceptions includes the studies by Desjardins, Dionne and Pinquet (2001), in which Bonus-Malus systems for fleets of vehicles are derived from the claims or safety offences history, and Pinquet (1997 and1998), in which examples is given of experience rating that incorporates additional claim information, from the number and the cost of claims, and claims at fault and not at fault within the same line of business. Instead of following the expected value principle, as in the latter papers, we follow the tradition of linear credibility.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Latent Risk: A Credibility Approach

Englund¹,

Guillén²,

Gustafsson³

et al. 2008

ASTIN Bull.

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“…Throughout the various examples, we present this kind of statistical tools for a posteriori rating. Useful references that discuss various aspects of a posteriori rating include, but are not limited to, Pinquet (1997Pinquet ( , 1998, Frees et al (1999), Pinquet et al (2001), Bolancé et al (2003) and Antonio and Beirlant (2007).…”

Section: Risk Classification and A Posteriori Ratingmentioning

confidence: 99%

Statistical concepts of a priori and a posteriori risk classification in insurance

Antonio

Valdez

2011

AStA Adv Stat Anal

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Everyday we face all kinds of risks, and insurance is in the business of providing us a means to transfer or share these risks, usually to eliminate or reduce the resulting financial burden, in exchange for a predetermined price or tariff. Actuaries are considered professional experts in the economic assessment of uncertain events, and equipped with many statistical tools for analytics, they help formulate a fair and reasonable tariff associated with these risks. An important part of the process of establishing fair insurance tariffs is risk classification, which involves the grouping of risks into various classes that share a homogeneous set of characteristics allowing the actuary to reasonably price discriminate. This article is a survey paper on the statistical tools for risk classification used in insurance. Because of recent availability of more complex data in the industry together with the technology to analyze these data, we additionally discuss modern techniques that have recently emerged in the statistics discipline and can be used for risk classification. While several of the illustrations discussed in the paper focus on general, or non-life, insurance, several of the principles we examine can be similarly applied to life insurance. Furthermore, we also distinguish between a priori and a posteriori ratemaking. The former is a process which forms the basis for ratemaking when a policyholder is new and insufficient information may be available. The latter process uses additional historical information about policyholder claims when this becomes available. In effect, the resulting a posteriori premium allows one to correct and adjust the previous a priori premium making the price discrimination even more fair and reasonable.

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Designing Optimal Bonus-Malus Systems from Different Types of Claims

Cited by 52 publications

References 6 publications

Hierarchical Insurance Claims Modeling

Hierarchical Insurance Claims Modeling

Multivariate Latent Risk: A Credibility Approach

Statistical concepts of a priori and a posteriori risk classification in insurance

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