Bonus-Malus Systems in Automobile Insurance
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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INTRODUCTION DEFINITION OF A BONUSMALUS SYSTEM
A TYPICAL BONUSMALUS EVOLUTION THE BELGIAN CASE
MODELS FOR THE CLAIM NUMBER DISTRIBUTION
APPLICATIONS IN OTHER DISCIPLINES
EVALUATION OF BONUSMALUS SYSTEMS
TOOL 1 THE RELATIVE STATIONARY AVERAGE LEVEL
TOOL 2 THE COEFFICIENT OF VARIATION OF THE INSUREDS PREMIUMS
TOOL 3 THE ELASTICITY OF A BONUSMALUS SYSTEM
CONSTRUCTION OF AN OPTIMAL SYSTEM EXPECTED VALUE PRINCIPLE
OTHER LOSS FUNCTIONS OTHER PREMIUM CALCULATION PRINCIPLES
PENALIZATION OF OVERCHARGES
ALLOWANCE FOR THE SEVERITY OF CLAIMS
THE EFFECT OF EXPENSE LOADINGS
AN ALTERNATIVE PROPOSAL A HIGH DEDUCTIBLE
A HIGHDEDUCTIBLE SYSTEM
EMPIRICAL DETERMINATION OF THE DEDUCTIBLE
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accident actuarial science analysis assumed ASTIN Bulletin asymptotic Automobile Insurance average optimal retention average premium basic premium Belgian BMS Belgium benchmark BMS classes bodily injury chapter claim amount claim frequency claim number claims history Class Premium Class coefficient of variation commercial premium computed consecutive claim-free correlation cost countries decreases defined discount factor Distribution of Number elasticity evaluate Expected Payments expense loading Exponential Utility Figure Fitted Distribution Gamma Gamma distribution high deductible increases Index of Toughness Lemaire loss function malus Markov chain mixed Poisson negative binomial distribution negative binomial model number of claims optimal BMS Optimal Bonus-Malus System optimal deductible parameters penalized penalty percent Poisson distribution portfolio posteriori premium calculation principle premium level principal components priori probability rate of convergence regression component risk premium RSAL selected Starting class stationary distribution statistical strategy structure function Sundt surcharge System Class Premium Table transition rules variance Willmot