Automobile Insurance: Actuarial Models (Huebner International Series on Risk, Insurance and Economic Security (4))

The mathematical theory of non-life insurance developed much later than the theory of life insurance. The problems that occur in the former field are far more intricate for several reasons: 1. In the field oflife insurance, the company usually has to pay a claim on the policy only once: the insured dies or the policy matures only once. It is with only a few particular types of policy (for instance, sickness insurance, when the insured starts working again after a period of sickness) that a valid claim can be made on a number of different occasions. On the other hand, the general rule in non-life insurance is that the policyholder is liable to be the victim of several losses (in automobile insurance, of course, but also in burglary and fire insurance, householders' comprehensive insurance, and so on). 2. In the field of life insurance, the amount to be paid by the company­ excluding any bonuses-is determined at the inception of the policy. For the various types of life insurance contracts, the sum payable on death or at maturity of the policy is known in advance. In the field of non-life insurance, the amount of a loss is a random variable: the cost of an automobile crash, the partial or totalloss of a building as a result of fire, the number and nature of injuries, and so forth. Front Matter....Pages i-xvii Front Matter....Pages 1-2 Belgium....Pages 3-15 Europe....Pages 17-38 North America....Pages 39-55 Front Matter....Pages 63-63 Statistical Bases....Pages 65-67 Number or Amount of Claim....Pages 69-70 Claim Frequency, Average Cost per Claim, and Pure Premium....Pages 71-79 Criticism of the Belgian Tariff....Pages 81-85 Selection of the Significant Variables....Pages 87-91 Use of the Results of a Sample Survey....Pages 93-100 Criticism of Regression Analysis Selection Methods....Pages 101-105 Application: Improvement in Underwriting Procedures....Pages 107-109 Front Matter....Pages 115-115 Introduction: The Negative Binomial Model....Pages 117-127 Construction of an Optimal Bonus-Malus System....Pages 129-137 Other Loss Functions: Other Premium Calculation Principles....Pages 139-149 Penalization of Overcharges....Pages 151-156 Allowance for Severity of Claims....Pages 157-162 Efficiency Measures of a Bonus-Malus System....Pages 163-171 Analysis of the Hunger for Bonus....Pages 173-184 The Effect of Expense Loadings....Pages 185-192 Epilogue: Construction of the New Belgian Bonus-Malus System....Pages 193-202 Front Matter....Pages 203-203 The Main Statistical Methods....Pages 205-230 An Example....Pages 231-240 Back Matter....Pages 241-249