The fundamental role of insurance is to provide financial protection, offering a method of transferring the risk in
exchange of an insurance premium. Considering that not all the risks are equal, it is natural that every insured will
pay a premium or tariff corresponding with the gravity of the risk.
The different charging tariffs are emphasized by the insurance portfolio heterogeneity that leads directly to antiselection
phenomenon. This basically presumes charging same tariff for the entire portfolio, meaning that the unfavorable risks are also assured (at a lower price) and as an adverse effect, it discourages insuring medium risks.
The necessity of pricing for non-life insurance comes precisely in an attempt to combat the anti-selection
phenomenon by dividing the insurance portfolio in sub-portfolios based on certain influence factors. Therefore,
every class will contain policyholders with identical risk profile that will pay the same reasonable premium.
A usual method to calculate the premium is to combine the conditional expectation of the claim frequency with
the expected cost of claims, considering the observable risk characteristics. The process of evaluating risks in order
to determine the insurance premium is performed by the actuaries, which over time proposed and applied different
statistical models. In this context, linear regression, used to evaluate the impact of explanatory variables on the
phenomenon of interest (studied risk), has been replaced starting with 1980 by the Generalized Linear Models
(GLMs). GLMs allow modeling a non-linear behavior and a non-Gaussian distribution of residuals. This aspect is
very useful for the analysis of non-life insurance, where claim frequency and claim cost follow an asymmetric
density that is clearly non-Gaussian. GLMs development has contributed to quality improvement of the risk
prediction models and to the process of establishing a fair tariff or premium given the nature of the risk.
The main objective of this paper is to apply GLM models in order to assess the premiums applied to each insured,
in an equitable and reasonable manner. In this purpose, the paper is structured as follows. Section 2 presents a brief
review of the literature regarding the approach of GLMs in non-life insurance pricing. Section 3 describes the
methodological framework used in this paper. Each subsection of this part analyzes the estimation methods of
frequency and cost of claims, leading to the calculation model of the pure premium. Section 4 is dedicated to a study
applied to auto insurance branch in order to highlight how to identify the risk factors that allow dividing the
insurance portfolio in tariff classes and how to obtain the corresponding pure premium. Section 5 presents the main
conclusions of the study.
The fundamental role of insurance is to provide financial protection, offering a method of transferring the risk inexchange of an insurance premium. Considering that not all the risks are equal, it is natural that every insured willpay a premium or tariff corresponding with the gravity of the risk.The different charging tariffs are emphasized by the insurance portfolio heterogeneity that leads directly to antiselectionphenomenon. This basically presumes charging same tariff for the entire portfolio, meaning that the unfavorable risks are also assured (at a lower price) and as an adverse effect, it discourages insuring medium risks.The necessity of pricing for non-life insurance comes precisely in an attempt to combat the anti-selectionphenomenon by dividing the insurance portfolio in sub-portfolios based on certain influence factors. Therefore,every class will contain policyholders with identical risk profile that will pay the same reasonable premium.A usual method to calculate the premium is to combine the conditional expectation of the claim frequency withthe expected cost of claims, considering the observable risk characteristics. The process of evaluating risks in orderto determine the insurance premium is performed by the actuaries, which over time proposed and applied differentstatistical models. In this context, linear regression, used to evaluate the impact of explanatory variables on thephenomenon of interest (studied risk), has been replaced starting with 1980 by the Generalized Linear Models(GLMs). GLMs allow modeling a non-linear behavior and a non-Gaussian distribution of residuals. This aspect isvery useful for the analysis of non-life insurance, where claim frequency and claim cost follow an asymmetricdensity that is clearly non-Gaussian. GLMs development has contributed to quality improvement of the riskprediction models and to the process of establishing a fair tariff or premium given the nature of the risk.The main objective of this paper is to apply GLM models in order to assess the premiums applied to each insured,in an equitable and reasonable manner. In this purpose, the paper is structured as follows. Section 2 presents a briefreview of the literature regarding the approach of GLMs in non-life insurance pricing. Section 3 describes themethodological framework used in this paper. Each subsection of this part analyzes the estimation methods offrequency and cost of claims, leading to the calculation model of the pure premium. Section 4 is dedicated to a studyapplied to auto insurance branch in order to highlight how to identify the risk factors that allow dividing theinsurance portfolio in tariff classes and how to obtain the corresponding pure premium. Section 5 presents the mainconclusions of the study.
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