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

Abstract

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.

A data driven binning strategy for the construction of insurance tariff classes

“…Following McClenahan (2001); Antonio and Valdez (2012) we denote with F i and S i respectively the frequency and severity of policyholder i. Frequency is expressed as the number of claims N i per unit of exposure e i , while severity is expressed as the average claim amount over the number of claims N i .…”

“…Premiums are equal for policyholders within the same tariff class and should reflect the inherent riskiness of each class. The process of constructing these tariff classes is also known as risk classification, see Denuit et al (2007); Antonio and Valdez (2012); Paefgen et al (2013). Pricing (or: ratemaking, tarification) through detailed risk classification is the mechanism for insurance companies to compete and to reduce the cost of insurance contracts.…”

The Application of Bühlmann-Straub Model to the Estimation of Net Premium Rates Depending on the Age of the Insured in the Motor Hull Liability Insurance

“…The first, called a priori ratemaking is the determination of net premiums, using actuarial methods (Antonio, Valdez 2012) based on certain risk factors, known as the basic ratemaking variables. The premium so defined increased, among others, by the costs of insurance operations and the security addition is known as the base premium.…”

Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models

“…Working with cross-sectional insurance data, Boucher et al (2007) sustain that the comparison of the log-likelihoods for the two distributions reveals that the extra parameter of the negative binomial distribution improves the fit of data in comparison with the Poisson distribution. For longitudinal or panel data, an excellent account of claim frequency distributions can be consulted in Boucher et al (2008), Boucher and Guillen (2009) and Antonio and Valdez (2010), in which the authors analyse and emphasize the practical use of negative binomial models for auto insurance data.…”

“…A standard classification would include: age and gender-marital status of insured, usage purpose of the insured vehicle, geography (location of garage) and other factors such as whether the vehicle is a sport car or not (Antonio and Valdez, 2010). A more systematic classification is provided by Kouki (2007) who identifies three categories of risk factors: the driver (age, sex, age of driving license, bonus-malus coefficient), the vehicle (power, age) and the insurance contract.…”