Jean Lemaire

Bonus-Malus Systems in Automobile Insurance

List of Figures. List of Tables. Preface. Part I: Introduction -- Models for Claim Number Distributions. 1. Introduction -- Definition of a Bonus-Malus System. 2. A Typical Bonus-Malus Evolution: the Belgian Case. 3. Models for the Claim Number Distribution. Appendix I. Part II: Evaluation of Bonus-Malus Systems. 4. Tool #1: The Relative Stationary Average Level. 5. Tool #2: The Coefficient of Variation of the Insureds Premium. 6. Tool #3: The Elasticity of the Bonus-Malus System. 7. Tool #4: The Average Optimal Retention. 8. An Index of Toughness. 9. Comments for Specific Countries. Rate of Convergence. Appendix II. Part III: The Design of an Optimal Bonus-Malus System. 10. Construction of an Optimal System. Expected Value Principle. 11. Other Loss Functions. Other Premium Calculation Principles. 12. Penalization of Overcharges. 13. Allowance for the Severity of Claims. 14. The Effect of Expense Loadings. Part IV: An Alternative Proposal: a High Deductible. 15. A High Deductibe System. 16. Empirical Determination of a Deductible. References. Author Index. Subject Index. Main Notations.

Automobile insurance : actuarial models

1 Belgium.- 2 Europe.- 3 North America.- 4 Statistical Bases.- 5 Number or Amount of Claim?.- 6 Claim Frequency, Average Cost per Claim, and Pure Premium.- 7 Criticism of the Belgian Tariff.- 8 Selection of the Significant Variables.- 9 Use of the Results of a Sample Survey.- 10 Criticism of Regression Analysis Selection Methods.- 11 Application: Improvement in Underwriting Procedures.- 12 Introduction: The Negative Binomial Model.- 13 Construction of an Optimal Bonus-Malus System.- 14 Other Loss Functions: Other Premium Calculation Principles.- 15 Penalization of Overcharges.- 16 Allowance for Severity of Claims.- 17 Efficiency Measures of a Bonus-Malus System.- 18 Analysis of the Hunger for Bonus.- 19 The Effect of Expense Loadings.- 20 Epilogue: Construction of The New Belgian Bonus-Malus System.- 21 The Main Statistical Methods.- 22 An Example.- References.- About the Author.

Life insurance and breast cancer risk assessment: adverse selection, genetic testing decisions, and discrimination.

Life insurance industry access to genetic information is controversial. Consumer groups argue that access will increase discrimination in life insurance premiums and discourage individuals from undergoing genetic testing that may provide health benefits. Conversely, life insurers argue that without access to risk information available to individuals, they face substantial financial risk from adverse selection. Given this controversy, we conducted a retrospective cohort study to evaluate the impact of breast cancer risk information on life insurance purchasing, the impact of concerns about life insurance discrimination on use of BRCA1/2 testing, and the incidence of life insurance discrimination following participation in breast cancer risk assessment and BRCA1/2 testing. Study participants were 636 women who participated in genetic counseling and/or genetic testing at a University based clinic offering breast cancer risk assessment, genetic counseling, and BRCA1/2 testing between January 1995 and May 2000. Twenty‐seven women (4%) had increased and six (1%) had decreased their life insurance since participation in breast cancer risk assessment. The decision to increase life insurance coverage was associated with predicted breast cancer risk (adjusted OR 1.03 for each 1% absolute increase in risk, 95% CI 1.01–1.10) and being found to carry a mutation in BRCA1/2 (OR 5.10, 95% CI 1.90–13.66). Concern about life insurance discrimination was inversely associated with the decision to undergo BRCA1/2 testing (RR 0.67, 95% CI 0.52–0.85). No respondent reported having life insurance denied or canceled. In this cohort of women, these results indicate that information about increased breast cancer risk is associated with increase in life insurance purchasing, raising the possibility of adverse selection. Although fear of insurance discrimination is associated with the decision not to undergo BRCA1/2 testing, there was no evidence of actual insurance discrimination from BRCA1/2 testing.

Cooperative Game Theory and its Insurance Applications

This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples.

The core of a reinsurance market

In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.

Adverse Selection in Term Life Insurance Purchasing Due to the Brca1/2 Genetic Test and Elastic Demand

Consumer groups fear that the use of genetic testing information in insurance underwriting might lead to the creation of an underclass of individuals who cannot obtain insurance; thus, these groups want to ban insurance companies from accessing genetic test results. Insurers contend that such a ban might lead to adverse selection that could threaten their financial solvency. To investigate the potential effect of adverse selection in a term life insurance market, a discrete-time, discrete-state, Markov chain is used to track the evolution of twelve closed cohorts of women, differentiated by family history of breast and ovarian cancer and age at issue of a 20-year annually renewable term life insurance policy. The insurance demand behavior of these women is tracked, incorporating elastic demand for insurance. During the 20-year period, women may get tested for BRCA1/2 mutations. Each year, the insurer calculates the expected premiums and expected future benefit payouts which determine the following years premium schedule. At the end of each policy year, women can change their life insurance benefit, influenced by their testing status and premium changes. Adverse selection could result from (i) differentiated benefits following test results; (ii) differentiated lapse rates according to test results; and (iii) differentiated reactions to price increases. It is concluded that with realistic estimates of behavioral parameters, adverse selection could be a manageable problem for insurers.

Reducing firearm violence: a research agenda

In the United States, firearms are involved in tens of thousands of deaths and injuries each year. The magnitude of this problem prompted the National Academy of Sciences (NAS) to issue a report in 2004 detailing the strengths and limitations of existing research on the relationship between firearms and violence. In response, a multidisciplinary group of experts in the field of firearms and violence formed the National Research Collaborative on Firearm Violence. The Collaborative met for 2 days in June 2005 to (1) critically review the main findings of the NAS report and (2) define a research agenda that could fill research and data gaps and inform policy that reduces gun-related crime, deaths and injuries. This article summarizes the Collaborative’s conclusions and identifies priorities for research and funding.

La Soif du Bonus

In motorcar insurance is widely used a merit rating system characterized by the fact that only the number of claims occurred (and not their amount) modifies the premium. This system induces the insured drivers to support themselves the cost of the cheap claims. We analyze this “hunger for bonus†and solve this decision problem by means of an algorithm related to dynamic programming. The method is then applied to the Belgian bonus system.

The Bargaining Set of a Reinsurance Market

This paper uses the same notations and some of the results of Baton and Lemaire (1981). The reader is referred to that work for more details about the classical risk exchange model, which will not be recalled here. The main result of that former paper was to characterize the core of the market in the case of exponential utilities, and to show that it is never empty. Since the core always exists, and since it is such an intuitive notion, one might wonder why we introduce here a much more complicated concept. The reason is that the core is presently subject to a heavy fire of criticisms–both experimental and theoretical–from leading researchers in game theory; they claim that the core is much too static, that it does not take into account the real dynamics of the bargaining process, that it does not introduce the full spectrum of negotiation threats of the traders. Indeed, experimental data consistently produce final payoffs that lie outside the core, but within the bargaining set (abbreviated: b.s.). We shall attempt to illustrate those criticisms in 4. We shall define the b.s. in a general non transferable game in 2, and characterize it in the special case of a 3-company reinsurance market in 3, but first of all we would like to explain intuitively the basic mechanisms of the b.s. by means of a simple example (with transferable utilities).The basic difficulty in modelling a negotiation process is to express what is the purpose of the game. Certainly, the objective is not just to get the maximal amount of profits, because if everyone demands the highest payoff he can obtain in a coalition, no agreement will be reached; the goal of the process is to attain some state of stability, to which the bargainers should agree if they want any agreement to be enforced. This stability should reflect in some way the power of each player, which results from the rules of the game, his initial situation, his attitude towards risk, …A bargaining process is a multi-criteria situation, in which the players certainly attempt to maximize their payoffs, but also try to enter into a “safe†or “stable†coalition.

A Comparative Analysis of Most European and Japanese Bonus-malus Systems

The bonus-malus systems of 13 different countries are presented and compared, using the following criteria: (1) stationary distribution of the policyholders among the classes, (2) elasticity of the premiums with respect to the claim frequency (efficiency), and (3) magnitude of the hunger for bonus.