Generalized Linear Models and Actuarial Science

Haberman, Steven; Renshaw, A. E.

doi:10.2307/2988543

Cited by 150 publications

(96 citation statements)

References 21 publications

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“…Haberman and Renshaw (1996) and references therein). In the framework of actuarial applications, there are several attempts to use GLM in order to describe the claim frequency, the claim size or other characteristics of a portfolio.…”

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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Section: Introductionmentioning

confidence: 99%

Modelling losses using an exponential-inverse Gaussian distribution

Frangos

Karlis

2004

Insurance: Mathematics and Economics

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“…The paper by Haberman and Renshaw (1996) provides an overview of its applications in actuarial science. Additional discussion of GLMs with an actuarial bent can be found in de Jong and Heller (2008), Frees (2010) and Kaas et al (2008).…”

Section: Current Practice: Generalized Linear Models (Glms)mentioning

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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“…These contained studies on general aspect of the GLM and its application on different real life situations [19], [40], [43], [26], [11] etc. There had been works based on the GLM for specific distributions also.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Generalized Linear Model for the Geometric Distribution

2016

Jour. Stat. Adv. Theory and Appl.

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Application of the generalized linear models (GLMs) in real life problems are well established and has extensive use. However, the GLM for the geometric distribution is not explored yet. The present study consists of the derivation of the GLM for the geometric distribution, estimation of parameters, and testprocedures. An application is made to Bangladesh Demographic and Health Survey 2011 data to find the significant factors associated with the first occurrence of infant death in terms of birth order. Two different generalized linear models are fitted, one using the natural link function and the other one using the log link function. At the end, the results of both models are compared.It is found that the model fitted using log link function has lower Akaike's information criteria (AIC) and deviance than the model fitted using the natural link function, that means the GLM for the geometric distribution using log link function provides better result.FARZANA JAHAN et al. 46

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Generalized Linear Models and Actuarial Science

Cited by 150 publications

References 21 publications

Modelling losses using an exponential-inverse Gaussian distribution

Modelling losses using an exponential-inverse Gaussian distribution

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

An Application of the Generalized Linear Model for the Geometric Distribution

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