Bonus-Malus Systems in Automobile Insurance

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Springer Science & Business Media, Apr 30, 1995 - Business & Economics - 283 pages
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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.
 

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Contents

INTRODUCTION DEFINITION OF A BONUSMALUS SYSTEM
3
A TYPICAL BONUSMALUS EVOLUTION THE BELGIAN CASE
11
MODELS FOR THE CLAIM NUMBER DISTRIBUTION
21
APPLICATIONS IN OTHER DISCIPLINES
43
EVALUATION OF BONUSMALUS SYSTEMS
57
TOOL 1 THE RELATIVE STATIONARY AVERAGE LEVEL
59
TOOL 2 THE COEFFICIENT OF VARIATION OF THE INSUREDS PREMIUMS
67
TOOL 3 THE ELASTICITY OF A BONUSMALUS SYSTEM
71
CONSTRUCTION OF AN OPTIMAL SYSTEM EXPECTED VALUE PRINCIPLE
155
OTHER LOSS FUNCTIONS OTHER PREMIUM CALCULATION PRINCIPLES
183
PENALIZATION OF OVERCHARGES
197
ALLOWANCE FOR THE SEVERITY OF CLAIMS
205
THE EFFECT OF EXPENSE LOADINGS
211
AN ALTERNATIVE PROPOSAL A HIGH DEDUCTIBLE
221
A HIGHDEDUCTIBLE SYSTEM
223
EMPIRICAL DETERMINATION OF THE DEDUCTIBLE
245

TOOL 4 THE AVERAGE OPTIMAL RETENTION
91
AN INDEX OF TOUGHNESS
103
COMMENTS FOR SPECIFIC COUNTRIES RATE OF CONVERGENCE
117
DESCRIPTION OF ALL BONUSMALUS SYSTEMS
133
THE DESIGN OF AN OPTIMAL BONUSMALUS SYSTEM
153
REFERENCES
257
AUTHOR INDEX
271
SUBJECT INDEX
277
ABOUT THE AUTHOR
285
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