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I argue that the idea of pursuing a strong personalization of the motor liability insurance conflicts hopelessly with the need to refer to homogeneous groups of policyholders large enough to be correctly priced. I furthermore discuss the fact that, due to purely algebraic reasons, it is a priori impossible to obtain the right individual premium by the usual method of multiplying a common base one by a series of factors (as many, as the personalization variables one has chosen to consider). Finally, I point out that the choice of the said factors, not always made with sufficient respect for the statistical evidences, not only gives rise to serious problems concerning the system's fairness and transparency, but puts theoretically at risk the Companies management balance. [ABSTRACT FROM AUTHOR]

In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS's basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significantly improves the prediction capacity of the BMS and provides a temporary solution for insurers who do not have enough historical data. We apply the BMS model to real data from a major Canadian insurance company. Results are analysed deeply to identify specific aspects of the BMS model. [ABSTRACT FROM AUTHOR]

How to consider the a priori risks in experience-rating models has been questioned in the actuarial community for a long time. Classic past-claim-rating models, such as the Buhlmann–Straub credibility model, normalize the past experience of each insured before applying claim penalties. On the other hand, classic Bonus–Malus Scales (BMS) models generate the same surcharges and the same discounts for all insureds because the transition rules within the class system do not depend on the a priori risk. Despite the quality of prediction of the BMS models, this experience-rating model could appear unfair to many insureds and regulators because it does not recognize the initial risk of the insured. In this paper, we propose the creation of different BMSs for each type of insured using recursive partitioning methods. We apply this approach to real data for the farm insurance product of a major Canadian insurance company with widely varying sizes of insureds. Because the a priori risk can change over time, a study of the possible transitions between different BMS models is also performed. [ABSTRACT FROM AUTHOR]

How to consider the a priori risks in experience-rating models has been questioned in the actuarial community for a long time. Classic past-claim-rating models, such as the Buhlmann–Straub credibility model, normalize the past experience of each insured before applying claim penalties. On the other hand, classic Bonus–Malus Scales (BMS) models generate the same surcharges and the same discounts for all insureds because the transition rules within the class system do not depend on the a priori risk. Despite the quality of prediction of the BMS models, this experience-rating model could appear unfair to many insureds and regulators because it does not recognize the initial risk of the insured. In this paper, we propose the creation of different BMSs for each type of insured using recursive partitioning methods. We apply this approach to real data for the farm insurance product of a major Canadian insurance company with widely varying sizes of insureds. Because the a priori risk can change over time, a study of the possible transitions between different BMS models is also performed.

Obviously, the design of a bonus-malus system has to take into consideration all rating variables used by the auto insurance carrier. For instance, a single male urban driver is likely to be penalized twice, a priori through explicit surcharges linked to his risk class, and a posteriori through premium increases triggered by the transition rules of the bonus-malus system, creating the possibility of excessive premiums through double-counting for the same reason. Taylor (ASTIN Bull 27:319-327, ) developed a Bayesian model to evaluate the impact of covariate rating variables on bonus-malus premium levels, but could not access actual data to implement his model. We present the first real-life application of Taylor's research, by using a unique database originating from Taiwan and the bonus-malus system in force in this island. Our data combines car and insurance information from the leading insurer in the island with annual mileage readings from a network of repair shops operated by the largest car manufacturer-over a quarter million policy-years. Park et al. (The use of annual mileage as a rating variable. Working paper, ), using the same data, used negative binomial regression to prove that mileage is by far the best predictor of accidents. The application of Taylor's model concludes that the impact of mileage on bonus-malus premium levels is small. Therefore, double-counting should not be considered as a major concern in practice. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The conditional specification technique introduced by Arnold et al. (Conditional specification of statistical models. Springer series in statistics. Springer, New York, 1999) was used in Sarabia et al. (Astin Bull 34(1):85–98, 2004) to obtain bonus-malus premiums. The Poisson distribution for which the parameter is a function of the classical structure parameter was used and a new class of prior distributions appeared in a natural way. This model contains, as a particular case, the classical compound Poisson model. In the present paper, the Bayesian robustness of this new model is examined and found to be much more robust than in the classical model in Gómez et al. (Insur Math Econ 31:105–113, 2002). For the present study, the moment conditions on the prior distribution are required. Examples, with real data, are given to illustrate our ideas under the net and exponential premium principles. [ABSTRACT FROM AUTHOR]

A general framework for a Bonus–Malus system (BMS) based on the number and the size of the claims is presented, the set of the bonus classes being an interval [ a ,? b ], say 0 < a < 1 < b . The BMS is interpreted as a general Markov chain with state space [ a ,? b ]. It turns out that, under certain assumptions, the Markov chain possesses an invariant limit distribution to which it converges with a geometric rate. We show how the invariant distribution can be evaluated by means of simulation. We also deal with the best possible convergence rate and show how it can be presented by means of the spectral theory of Banach spaces. [ABSTRACT FROM AUTHOR]

In a deregulated insurance market, insurance carriers have an incentive to be innovative in their pricing decisions by segmenting their portfolios and designing new bonus-malus systems (BMS). This paper examines the evolution of market shares and claim frequencies in a two-company market, when one insurer breaks off the existing stability by introducing a super-discount class in its BMS. Several assumptions concerning policyholders and insurers behavior are tested. Diffusion theory is used to model the spread of the information concerning the new BMS among prospective customers. A wide variety of market outcomes results: one company may take over the market or the two may survive with equal or unequal market shares, each specializing in a specific niche of the market. Before engaging in an aggressive competitive behavior, insurers should consequently be reasonably confident in their assumptions concerning the reactions of their policyholders to the new BMS. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show how linear programming methodology can help us to design Bonus-Malus premium scales with some interesting theoretical and practical attributes. Examples of these properties are the financial equilibrium of the system, the monotonicity and proper variability of the premium scale, and the improvement of some efficiency measures such as the RSAL and the elasticity of the system. We will conclude that the use of the linear programming methodology makes possible a high degree of interaction between the designer and the mathematical model. [ABSTRACT FROM AUTHOR]

In this paper a new methodology using the conditional specification technique introduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas. [ABSTRACT FROM AUTHOR]