Actuarial Modelling of Claim Counts Risk Classification Credibility and Bonus Malus Systems 1st Edition by Michel Denuit, Xavier Marechal, Sandra Pitrebois ISBN 0470026774 9780470026779

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ISBN 10: 0470026774 
ISBN 13: 9780470026779
Author: Michel Denuit, Xavier Marechal, Sandra Pitrebois

There are a wide range of variables for actuaries to consider when calculating 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 a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information.

The text:

• Offers the first self-contained, practical approach to a priori and a posteriori ratemaking in motor insurance.
• Discusses the issues of claim frequency and claim severity, multi-event systems, and the combinations of deductibles and BMSs.
• Introduces recent developments in actuarial science and exploits the generalised linear model and generalised linear mixed model to achieve risk classification.
• Presents credibility mechanisms as refinements of commercial BMSs.
• Provides practical applications with real data sets processed with SAS software.

Actuarial Modelling of Claim Counts is essential reading for students in actuarial science, as well as practicing and academic actuaries. It is also ideally suited for professionals involved in the insurance industry, applied mathematicians, quantitative economists, financial engineers and statisticians.

Actuarial Modelling of Claim Counts Risk Classification Credibility and Bonus Malus Systems 1st Table of contents:

Part I: Risk Classification

1. Introduction to Risk Classification
   • The Need for Risk Classification in Insurance
   • Basic Concepts: Risk Factors, Homogeneity, Discrimination
   • Regulatory and Ethical Considerations
2. Generalized Linear Models (GLMs) for Claim Counts
   • Review of Linear Regression
   • Introduction to GLMs (Link Functions, Variance Functions)
   • Poisson Regression for Claim Counts
   • Negative Binomial Regression for Overdispersion
   • Model Building and Interpretation (Deviance, AIC, BIC)
3. Advanced GLM Topics and Extensions
   • Offset and Exposure
   • Interactions between Risk Factors
   • Non-Linear Effects of Continuous Covariates (e.g., Splines)
   • Handling Zero-Inflated and Hurdle Models
4. Tree-Based Methods for Risk Classification
   • Decision Trees (CART)
   • Random Forests
   • Gradient Boosting Machines (GBM, XGBoost, LightGBM)
   • Model Interpretability (Feature Importance, SHAP values)
5. Geographical Pricing and Spatial Models
   • The Importance of Location in Insurance Pricing
   • Spatial Smoothing Techniques
   • Geographical Information Systems (GIS) in Actuarial Modelling

Part II: Credibility Theory

6. Introduction to Credibility Theory
   • What is Credibility? Why is it Needed?
   • Balancing Prior Knowledge and Recent Experience
   • Bayesian vs. Classical Credibility
7. Classical Credibility (Limited Fluctuation Credibility)
   • Concept of Full Credibility
   • Partial Credibility Formulae (e.g., Normal Approximation)
   • Practical Applications and Limitations
8. Bayesian Credibility
   • Bayesian Inference Framework
   • Conjugate Priors and Posterior Distributions
   • Poisson-Gamma Model for Claim Counts
   • Normal-Normal Model
9. Bühlmann Credibility
   • Linear Approximation to Bayesian Estimators
   • Bühlmann’s Formula and Its Derivation
   • Estimation of Parameters (Variance Components)
   • Multi-Dimensional Bühlmann Models
10. Bühlmann-Straub Credibility
    • Extension of Bühlmann for Unequal Exposures
    • Application in Group Insurance and Self-Rated Exposures
11. Empirical Bayes Credibility
    • Estimating Credibility Parameters from Data
    • Applications and Examples
12. Credibility in GLM Context
    • Combining GLMs with Credibility Concepts
    • Credibility adjustments to GLM predictions.

Part III: Bonus-Malus Systems

13. Introduction to Bonus-Malus Systems (BMS)
    • Purpose and Objectives of BMS (Fairness, Incentive, Risk Adaptation)
    • Historical Overview and International Practices
    • Key Components of a BMS (States, Transition Rules, Discounts/Surcharges)
14. Theoretical Foundations of BMS
    • Markov Chains for BMS
    • Equilibrium Distribution of Policyholders
    • Premium Calculation under BMS
15. Optimal Bonus-Malus Systems
    • Designing BMS for Optimality (e.g., Bayesian Optimality)
    • The Poisson-Gamma Model for Optimal BMS
    • Beyond the Poisson-Gamma Assumptions
16. Practical Design and Implementation of BMS
    • Choosing the Number of States and Transition Rules
    • Setting Discounts and Surcharges
    • Impact on Policyholder Behavior and Adverse Selection
    • Regulatory Constraints and Consumer Acceptance
17. Advanced Topics in BMS
    • BMS for Multiple Lines of Business
    • BMS with Partial Claims (e.g., Glass Claims)
    • Telematics and Usage-Based Insurance (UBI) in BMS
    • Machine Learning Approaches to BMS Design

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Tags: Michel Denuit, Xavier Marechal, Sandra Pitrebois, Actuarial, Modelling