A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving

Verrall, Richard

doi:10.1080/10920277.2004.10596152

Cited by 61 publications

(63 citation statements)

References 8 publications

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“…Other possible approaches to modeling the dataset include Bayesian predictive modeling; see de Alba (2002) and Verrall (2004) for recent actuarial applications. Another approach would be to model the claims count for each of the three types jointly and thus consider a trivariate Poisson process.…”

Section: Inferencementioning

confidence: 99%

Hierarchical Insurance Claims Modeling

Frees

Valdez

2008

Journal of the American Statistical Association

162

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: Inferencementioning

confidence: 99%

Hierarchical Insurance Claims Modeling

Frees

Valdez

2008

Journal of the American Statistical Association

162

117

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“…However, the estimators of the mean square error of prediction are different to the ones given in Mack [10]. Moreover, we would like to remark that the Bayesian model considered in this paper is different to the Bayesian models considered for the increments D i, j = C i, j -C i, j -1 in Verrall [18] and [19] In the sequel it is useful to define for j = 0, …, J…”

Section: Classical Chain Laddermentioning

confidence: 99%

Credibility for the Chain Ladder Reserving Method

Gisler¹,

Wüthrich²

2008

ASTIN Bull.

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We consider the chain ladder reserving method in a Bayesian set up, which allows for combining the information from a specific claims development triangle with the information from a collective. That is, for instance, to consider simultaneously own company specific data and industry-wide data to estimate the own company's claims reserves. We derive Bayesian estimators and credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential dispersion family with its natural conjugate priors. Finally, we make the link to the classical chain ladder method and we show that using non-informative priors we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ in our Bayesian set up from the ones found in the literature. Hence, the paper also throws a new light upon the estimator of the mean square error of prediction of the classical chain ladder forecasts and suggests a new estimator in the chain ladder method.

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“…47 See e.g. DeAlba (2002Alba ( , 2006,Verrall (2004),Verrall and England (2005),Peters et al (2009), andVerrall et al (2011). 48 See e.g.…”

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confidence: 98%

Loss prediction based on run-off triangles

Schmidt

2011

AStA Adv Stat Anal

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Loss reserving is an important subject of actuarial mathematics. It aims at the prediction of future losses caused by claims which have incurred in the past but have not yet been closed. The problem of predicting such losses is particularly important in liability insurance. More generally, it is most relevant with respect to the new regulatory requirements for insurance companies operating in the European Union, which are known as Solvency II.

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A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving

Cited by 61 publications

References 8 publications

Hierarchical Insurance Claims Modeling

Hierarchical Insurance Claims Modeling

Credibility for the Chain Ladder Reserving Method

Loss prediction based on run-off triangles

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