Detailed Table of Contents

To understand the professional association requirements, hover the mouse over the hyperlinks ( for example, SoA-Proposal 3.3). They are not linked to any supporting pages!

Part A. Foundations

1. Introduction to Loss Data Analytics

  • Relevance of analytics

  • Variable types

  • Insurance company operations

    • Sets the stage for the text; introduces examples from ratemaking, claims management, and reserving

2. Modeling loss frequency

    • How frequency augments severity information

    • Basic frequency distributions: binomial, Poisson, negative binomial

3. Modeling loss severity

4. Model selection and comparison

  • Nonparametric estimation tools (moments, quantiles, distribution function and kernel density estimators)

  • Nonparametric estimation tools for model selection (graphical methods, goodness of fit statistics)

  • Nonparametric estimation using modified data (ogive, Kaplan-Meier, Nelson-Aalen)

  • Parametric (likelihood-based) estimation (with data that are individual and complete, grouped, censored, and/or truncated), including starting values based on method of moments and percentile matching

  • Introduction to Bayesian inference

    • Professional Association Learning Objectives: CAS Exam 4: F.1, G.1-2,5, SoA Exam C: F.1, H.1-2, SoA-Proposal: 3.7.17, IOA-CT6: v.1-5

5. Aggregate loss models

    • Individual risk model: convolution, approximate methods

    • Collective risk model: compound distributions, Panjer method, approximate methods

6. Simulation

    • Monte Carlo simulation

    • The inversion method and other methods

    • Estimating how many to simulate

    • Simulation error: mean squared error, estimation

Part B. Short term insurance

7. Premium calculation fundamentals

    • The concept of pure premium

8. Risk classification

  • Introduction to risk classification using Poisson regression models

  • Exposure to risk

  • Categorical variables and multiplicative tariff

  • Extensions to generalized linear models

Technical Supplement 3. Likelihood and generalized linear models

9. Experience rating using credibility theory

  • A posteriori premium rating and risk classification

  • Penalizing bad risks, rewarding good risks: updating loss frequency/severity

  • Shrinkage estimation: credibility theory (classical, Bühlmann credibility, Bayesian, empirical Bayes)

  • Credibility models expressed as regression and/or panel data models

  • Calculating relativities: a priori vs a posteriori

  • Prediction intervals

    • Professional Association Learning Objectives: CAS Exam 4: H.1-5, SoA Exam C: I.1-5, SoA Proposal: 3.7.3, 3.7.17-18, IOA-CT6: v.6-10, IAA Statistics: 2.4.2

10. Portfolio management, including reinsurance

    • Tails of distributions

  • Risk measures

  • Extreme value distributions

  • Reinsurance and layering effects

    • Professional Association Learning Objectives: CAS Exam 4: A.1,7, SoA Exam C: A.7,8, E.1, SoA Proposal: 3.7.4, 3.7.7, 3.7.14, 3.7.19-20

11. Loss reserving

  • Delays in reporting and settlement: Reported but not yet settled (RBNS) or Incurred but not yet reported (IBNR)

  • Calculation methods to predict outstanding or ultimate claims: chain-ladder, separation, Bornhuetter-Ferguson, average cost per claim

  • Alternative methods: Bayesian, stochastic

  • Testing adequacy of loss reserves

Part C. Advanced topics

12. Retention and experience rating using bonus-malus

  • Retention using logistic regression and stationary distributions

  • Bonus-malus or no claims discount systems: transition rules, transition probability, stationary distributions

13. Data and systems

14. Dependence modeling

15. Health Analytics

16. Topics in statistical inference, including GLM details

  • Bayes method

  • Boostrapping

  • Information criteria, Vuong's test

Appendices

Appendix A. Review of statistical inference

Appendix B. Iterated expectations

Appendix C. Maximum likelihood theory