Actuarial Modelling of Claim Counts
Risk Classification, Credibility and Bonus-Malus Systems
Published on 27. September 2007
384 pages
978-0-470-51741-3 (ISBN)
Description
There are a wide range of variables for actuaries to consider whencalculating a motorist's insurance premium, such as age,gender and type of vehicle. Further to these factors,motorists' rates are subject to experience rating systems,including credibility mechanisms and Bonus Malus systems (BMSs).
Actuarial Modelling of Claim Counts presents acomprehensive treatment of the various experience rating systemsand their relationships with risk classification. The authorssummarize the most recent developments in the field, presentingratemaking systems, whilst taking into account exogenousinformation.
The text:
* Offers the first self-contained, practical approach to a prioriand a posteriori ratemaking in motor insurance.
* Discusses the issues of claim frequency and claim severity,multi-event systems, and the combinations of deductibles andBMSs.
* Introduces recent developments in actuarial science andexploits the generalised linear model and generalised linear mixedmodel to achieve risk classification.
* Presents credibility mechanisms as refinements of commercialBMSs.
* Provides practical applications with real data sets processedwith SAS software.
Actuarial Modelling of Claim Counts is essential readingfor students in actuarial science, as well as practicing andacademic actuaries. It is also ideally suited for professionalsinvolved in the insurance industry, applied mathematicians,quantitative economists, financial engineers and statisticians.
Reviews / Votes
"An excellent text on experience rating that picks up the actuarial reader at almost every level. The authors have found an excellent balance between theory and practice." (Journal of the American Statistical Association, June 2009)More details
Other editions
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M. Denuit
Actuarial Modelling of Claim Counts - Risk Classification, Credibility and Bonus-Malus Systems
Software
11/2007
Wiley
€89.49
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Michel Denuit | Xavier Marechal | Sandra Pitrebois
Actuarial Modelling of Claim Counts
Risk Classification, Credibility and Bonus-Malus Systems
Book
08/2007
Wiley
€135.00
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Persons
Michel Denuit - Professor, Institute of ActuarialScience, UCL, Belgium.
Michel Denuit is Professor of Statistics and Actuarial Scienceat the Université Catholique de Louvain, Belgium. His majorfields of research are risk theory and stochastic inequalities. Hehas (co-)authored numerous articles that have appeared in appliedand theoretical journals and served as member of the editorialboard for several journals (including Insurance: Mathematics andEconomics). He is a section editor on Wiley's Encyclopedia ofActuarial Science, and is the author of two previous books, one ofthem with Wiley.
Xavier Maréchal - Université Catholiquede Louvain, Belgium & CEO of Reacfin, Belgium.
Sandra Pitrebois - Université Catholique deLouvain, Belgium & Secura Belgian Re, Brussels.
Jean-François Walhin - UniversitéCatholique de Louvain, Belgium & Secura Belgian Re,Brussels
Content
Foreword.
Preface.
Notation.
Part I Modelling Claim Counts.
1 Mixed Poisson Models for Claim Numbers.
1.1 Introduction.
1.2 Probabilistic Tools.
1.3 Poisson Distribution.
1.4 Mixed Poisson Distributions.
1.5 Statistical Inference for Discrete Distributions.
1.6 Numerical Illustration.
1.7 Further Reading and Bibliographic Notes.
2 Risk Classification.
2.1 Introduction.
2.2 Descriptive Statistics for Portfolio A.
2.3 Poisson Regression Model.
2.4 Overdispersion.
2.5 Negative Binomial Regression Model.
2.6 Poisson-Inverse Gaussian Regression Model.
2.7 Poisson-LogNormal Regression Model.
2.8 Risk Classification for Portfolio A.
2.9 Ratemaking using Panel Data.
2.10 Further Reading and Bibliographic Notes.
Part II Basics of Experience Rating.
3 Credibility Models for Claim Counts.
3.1 Introduction.
3.2 Credibility Models.
3.3 Credibility Formulas with a Quadratic Loss Function.
3.4 Credibility Formulas with an Exponential Loss Function.
3.5 Dependence in the Mixed Poisson Credibility Model.
3.6 Further Reading and Bibliographic Notes.
4 Bonus-Malus Scales.
4.1 Introduction.
4.2 Modelling Bonus-Malus Systems.
4.3 Transition Probabilities.
4.4 Long-Term Behaviour of Bonus-Malus Systems.
4.5 Relativities with a Quadratic Loss Function.
4.6 Relativities with an Exponential Loss Function.
4.7 Special Bonus Rule.
4.8 Change of Scale.
4.9 Dependence in Bonus-Malus Scales.
4.10 Further Reading and Bibliographic Notes.
Part III Advances in Experience Rating.
5 Efficiency and Bonus Hunger.
5.1 Introduction.
5.2 Modelling Claim Severities.
5.3 Measures of Efficiency for Bonus-Malus Scales.
5.4 Bonus Hunger and Optimal Retention.
5.5 Further Reading and Bibliographic Notes.
6 Multi-Event Systems.
6.1 Introduction.
6.2 Multi-Event Credibility Models.
6.3 Multi-Event Bonus-Malus Scales.
6.4 Further Reading and Bibliographic Notes.
7 Bonus-Malus Systems with Varying Deductibles.
7.1 Introduction.
7.2 Distribution of the Annual Aggregate Claims.
7.3 Introducing a Deductible within a PosterioriRatemaking.
7.4 Numerical Illustrations.
7.5 Further Reading and Bibliographic Notes.
8 Transient Maximum Accuracy Criterion.
8.1 Introduction.
8.2 Transient Behaviour and Convergence of Bonus-MalusScales.
8.3 Quadratic Loss Function.
8.4 Exponential Loss Function.
8.5 Numerical Illustrations.
8.6 Super Bonus Level.
8.7 Further Reading and Bibliographic Notes.
9 Actuarial Analysis of the French Bonus-MalusSystem.
9.1 Introduction.
9.2 French Bonus-Malus System.
9.3 Partial Liability.
9.4 Further Reading and Bibliographic Notes.
Bibliography.
Index.
