Burr regression and portfolio segmentation

Beirlant, Jan; Goegebeur, Yuri; Verlaak, Robert; Vynckier, Petra

doi:10.1016/s0167-6687(98)00045-6

Cited by 30 publications

(20 citation statements)

References 6 publications

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“…The …rst paper is due to McDonald and Butler (1990) who used the GB2 with regression covariates to examine the duration of welfare spells. Beirlant et al (1998) demonstrated the usefulness of the Burr XII distribution, a special case of the GB2 with 1 = 1, in regression applications. Recently, Sun et al (2006) used the GB2 in a longitudinal data context to forecast nursing home utilization.…”

Section: Severity 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: Severity Componentmentioning

confidence: 99%

Hierarchical Insurance Claims Modeling

Frees

Valdez

2008

Journal of the American Statistical Association

165

117

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“…Many of them are popular in survival analysis, too. Beirlant et al (1998) used a Burr regression model for portfolio segmentation purposes.…”

Section: Introductionmentioning

confidence: 99%

Modelling losses using an exponential-inverse Gaussian distribution

Frangos

Karlis

2004

Insurance: Mathematics and Economics

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An exponential-inverse Gaussian distribution is used to model the claim size distribution. The distribution has shorter tails than the Pareto distribution and it is considered as a plausible model for data without large tails. We present the model allowing for covariates. Properties of the model are discussed. An EM algorithm is provided to fit the model. The algorithm is quite simple and programmable without need for any special functions. The model can be seen as a random effect model for exponential survival times regression. A real data application using a car-insurance company portfolio data is provided.

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“…A special case of the GB2 class is the Burr Type XII distribution. The work of Beirlant et al (1998) introduces Burr regression in the actuarial literature.…”

Section: Risk Classificationmentioning

confidence: 99%

“…As an illustration of this approach, we consider a fire insurance portfolio (see Beirlant et al 1998) that consists of 1,823 observations. We want to assess how the loss distribution changes with the sum insured and the type of building.…”

Section: Risk Classificationmentioning

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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Burr regression and portfolio segmentation

Cited by 30 publications

References 6 publications

Hierarchical Insurance Claims Modeling

Hierarchical Insurance Claims Modeling

Modelling losses using an exponential-inverse Gaussian distribution

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

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