Bonus-malus Scale Research Articles

Bonus-Malus Scale premiums for Tweedie’s compound Poisson models

Abstract Based on the recent papers, two distributions for the total claims amount (loss cost) are considered: compound Poisson-gamma and Tweedie. Each is used as an underlying distribution in the Bonus-Malus Scale (BMS) model. The BMS model links the premium of an insurance contract to a function of the insurance experience of the related policy. In other words, the idea is to model the increase and the decrease in premiums for insureds who do or do not file claims. We applied our approach to a sample of data from a major insurance company in Canada. Data fit and predictability were analyzed. We showed that the studied models are exciting alternatives to consider from a practical point of view, and that predictive ratemaking models can address some important practical considerations.

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

With the emergence of telematics, huge amounts of data have become available to insurers, raising the question of their integration into motor insurance pricing. Near-claim events are dangerous events that could have triggered a claim. Typically, they correspond to harsh deceleration, acceleration, or cornering. Based on the motor third-party liability insurance portfolio of an insurance company operating in Belgium, we highlight that deceleration events are the best candidates for characterizing near-claim events. Then, we propose to integrate these events in the pricing structure in addition to a policyholder’s claim history with the help of a bivariate Poisson-Lognormal credibility model. Finally, we design an original bonus–malus scale based on both claim and near-claim events.

Bonus-Malus Scale models: creating artificial past claims history

AbstractIn 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.

Multiple Bonus–Malus Scale Models for Insureds of Different Sizes

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.

Bonus–malus systems with different claim types and varying deductibles

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bonus-malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus-malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.

MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

AbstractMotor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.

Further comments on the paper “Setting a bonus–malus scale in the presence of other rating factors” by Taylor

Further comments on the paper “Setting a bonus–malus scale in the presence of other rating factors” by Taylor

Do people drive safer when accidents are more expensive: Testing for moral hazard in experience rating schemes

Using individual policies and claims data from the Croatian mandatory motor insurance we test the theoretical proposition that under moral hazard, experience rated pricing scheme should generate the negative state dependence in claims, i.e. that drivers should drive more safely after they had an accident. The empirical challenge in these tests is to disentangle the state dependence from unobserved heterogeneity. We propose a simple approach based on the explicit reliance on the cost of future accidents function which is used to filter out the pure incentives effect, whereas the bonus-malus scale is used to control for pure heterogeneity. Our results confirm the existence of negative dependence in claims indicating the presence of significant moral hazard effect. Increasing a 3-year cost of having an accident by approximately US$20 decreases the probability of having an accident by 6.5%.

Quest for Optimal Bonus-Malus in Automobile Insurance in Developing Economies: An Actuarial Perspective

This paper evaluates the bonus-malus system in practice in the Nigerian motor insurance industry. It would appear that the regulation is a bit fluid so that what actually looks like a bonus-malus system is more like a rule of thumb as operators do not honor the industry agreed tariff. This paper constructs an alternative bonus-malus scale that has reasonable penalties and that is yet commercially feasible. The model can easily be replicated for other developing economies.

How to transfer policyholders from one bonus-malus scale to the other?

With the deregulation of bonus-malus systems in the EU, it is important to obtain rules in order to transfer policyholders from one bonus-malus scale to another. The present paper proposes a solution to this problem.

Setting a Bonus-Malus Scale in the Presence of Other Rating Factors: Taylor's Work Revisited

In this paper, we propose an analytic analogue to the simulation procedure described in Taylor (1997). We apply the formulas to a Belgian data set and discuss the interaction between a priori and a posteriori ratemakings.

Setting a Bonus-Malus Scale in the Presence of Other Rating Factors: Taylor's Work Revisited

In this paper, we propose an analytic analogue to the simulation procedure described in Taylor (1997). We apply the formulas to a Belgian data set and discuss the interaction between a priori and a posteriori ratemakings.

Bonus-Malus scales using exponential loss functions

This paper focuses on techniques for constructing Bonus-Malus systems in third party liability automobile insurance. Specifically, the article presents a practical method for constructing optimal Bonus-Malus scales with reasonable penalties that can be commercially implemented. For this purpose, the symmetry between the overcharges and the undercharges reflected in the usual quadratic loss function is broken through the introduction of parametric asymmetric loss functions of exponential type. The resulting system possesses the desirable financial stability property.

Setting a Bonus-Malus Scale in the Presence of other Rating Factors

The operation of a bonus-malus system, superimposed on a premium system involving a number of other rating variables, is considered. To the extent that good risks are rewarded in their base premiums, through the other rating variables, the size of the bonus they require for equity is reduced. This issue is discussed quantitatively, and a numerical example given.

092037 (M31, B41) Setting a bonus-malus scale in the presence of other rating factors : Taylor G.,Centre for Actuarial Studies, Research Paper No. 40, 1996

092037 (M31, B41) Setting a bonus-malus scale in the presence of other rating factors : Taylor G.,Centre for Actuarial Studies, Research Paper No. 40, 1996