Bonus-Malus Systems in Automobile Insurance (Huebner International Series on Risk, Insurance and Economic Security, 19)

Most insurers around the world have introduced some form of merit-rating in automobile third party liability insurance. Such systems, penalizing at-fault accidents by premium surcharges and rewarding claim-free years by discounts, are called bonus-malus systems (BMS) in Europe and Asia. With the current deregulation trends that concern most insurance markets around the world, many companies will need to develop their own BMS. The main objective of the book is to provide them models to design BMS that meet their objectives. Part I of the book contains an overall presentation of the pros and cons of merit-rating, a case study and a review of the different probability distributions that can be used to model the number of claims in an automobile portfolio. In Part II, 30 systems from 22 different countries, are evaluated and ranked according to their `toughness' towards policyholders. Four tools are created to evaluate that toughness and provide a tentative classification of all systems. Then, factor analysis is used to aggregate and summarize the data, and provide a final ranking of all systems. Part III is an up-to-date review of all the probability models that have been proposed for the design of an optimal BMS. The application of these models would enable the reader to devise the system that is ideally suited to the behavior of the policyholders of his own insurance company. Finally, Part IV analyses an alternative to BMS; the introduction of a policy with a deductible. Most insurers around the world have introduced some form of merit-rating in automobile third party liability insurance. Such systems, penalizing at-fault accidents by premium surcharges and rewarding claim-free years by discounts, are called bonus-malus systems (BMS) in Europe and Asia. With the current deregulation trends that concern most insurance markets around the world, many companies will need to develop their own BMS. The main objective of the book is to provide them models to design BMS that meet their objectives. Part I of the book contains an overall presentation of the pros and cons of merit-rating, a case study and a review of the different probability distributions that can be used to model the number of claims in an automobile portfolio. In Part II, 30 systems from 22 different countries, are evaluated and ranked according to their 'stoughness' towards policyholders. Four tools are created to evaluate that toughness and provide a tentative classification of all systems. Then, factor analysis is used to aggregate and summarize the data, and provide a final ranking of all systems. Part III is an up-to-date review of all the probability models that have been proposed for the design of an optimal BMS. The application of these models would enable the reader to devise the system that is ideally suited to the behavior of the policyholders of his own insurance company. Finally, Part IV analyses an alternative to BMS; the introduction of a policy with a deductible Front Matter....Pages i-xxvi Front Matter....Pages 1-1 Introduction — Definition of a Bonus-Malus System....Pages 3-10 A Typical Bonus-Malus Evolution: The Belgian Case....Pages 11-19 Models for the Claim Number Distribution....Pages 21-42 Back Matter....Pages 43-56 Front Matter....Pages 57-57 Tool 1: The Relative Stationary Average Level....Pages 59-66 Tool 2: The Coefficient of Variation of the Insured’s Premiums....Pages 67-70 Tool 3: The Elasticity of a Bonus-Malus System....Pages 71-89 Tool 4: The Average Optimal Retention....Pages 91-102 An Index of Toughness....Pages 103-115 Comments for Specific Countries. Rate of Convergence....Pages 117-131 Back Matter....Pages 133-152 Front Matter....Pages 153-153 Construction of an Optimal System. Expected Value Principle....Pages 155-181 Other Loss Functions. Other Premium Calculation Principles....Pages 183-196 Penalization of Overcharges....Pages 197-204 Allowance for the Severity of Claims....Pages 205-210 The Effect of Expense Loadings....Pages 211-220 Front Matter....Pages 221-221 A High-Deductible System....Pages 223-244 Empirical Determination of the Deductible....Pages 245-256 Back Matter....Pages 257-285