Ebook: Automobile Insurance: Actuarial Models

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.

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Content:
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

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Content:
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
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