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
The (a,b,0) class of distributions
Estimating frequency models using maximum likelihood
Additional distributions: zero-inflated, modified, and truncated models and mixtures (e.g. Poisson-gamma)
Model selection and comparison
Professional Association Learning Objectives: CAS-Exam 4 B.1, SoA- Exam C: B.1-5, SoA-Proposal:3.7.8-9, IOA-CT6: iii.1-7, IAA-Models: 6.3
3. Modeling loss severity
Basic severity distributions: gamma, Pareto, GB2, Weibull
Methods of creating new distributions: transformation, mixture, spliced distributions
Maximum likelihood estimation and model comparison
Coverage modifications: policy deductible, policy limit
Maximum likelihood estimation with censored and truncated data
Professional Association Learning Objectives: CAS Exam 4:D.1, SoA Exam C: D.1, SoA-Proposal:3.7.4-6), SoA Exam C: H.2, SoA-Proposal 3.3 SoA-Proposal:3.7.13, CAS Exam 4:A.1-7, SoA Exam C: A.1-8, SoA-Proposal:3.7.4-6, IOA-CT6: ii.1-7,iii.1-7, IAA-Models: 6.2
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
Relationship between individual and collective risk models
Methods to create new count distributions: mixtures and hurdle models
Effects of deductibles
Tweedie and other compound models
Professional Association Learning Objectives: CAS Exam 4:C.1-3, SoA Exam C:C.1-3, SoA-Proposal:3.7.10-11, IOA-CT6: ii.1-7,iii.1-7, IAA-Models: 6.4
6. Simulation
Monte Carlo simulation
The inversion method and other methods
Estimating how many to simulate
Simulation error: mean squared error, estimation
Applications of simulation in insurance and finance
Bootstrapping
Cross-validation
Monte Carlo Markov Chain (MCMC) ???
Professional Association Learning Objectives: CAS Exam 4:I.1-5, SoA Exam C:J.1-6, SoA-Proposal:3.8.4-5, IOA-CT6: ix.1-3, IAA-Stats 2.6
Part B. Short term insurance
7. Premium calculation fundamentals
The concept of pure premium
The two-part model: claim frequency, severity given frequency
Estimation and inference
Effects of coverage modifications, including inflation (also loss elimination ratio)
Other methods: loss ratio
Professional Association Learning Objectives: SoA-Proposal:3.7.15, CAS Exam 4:D.2-3, ( SoA Exam C:D.1,2, SoA-Proposal:3.7.4-6, IOA-CT6: ii.1-7,iii.1-7, IAA-Models: 6.2 SoA-Proposal:3.7.4 IOA-CT6: ii.5,
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
Professional Association Learning Objectives: IAA B.6. Data and Systems, IFoA 2019 CS2 - Actuarial Statistics - 5. Machine Learning, SoA Statistics for Risk Modeling - 1. Basics of Statistical Learning
14. Dependence modeling
Professional Association Learning Objectives: IFoA 2019 CS2 - Actuarial Statistics -1.3 Introduction to copulas
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
Random sampling, sampling distributions, central limit theorem
Point estimation and properties: method of moments, maximum likelihood
Interval estimation: standard errors, large sample properties
Hypothesis testing: Neyman Pearson lemma, level of significance, power, likelihood ratio test, information criteria
Professional Association Learning Objectives: SoA-Proposal 3.3, IAA-Stats 2.2, CAS Exam S:B-Stats 2, CAS Exam S:B-Stats 1,4, SoA-C: H.1,H.3
Appendix B. Iterated expectations
Appendix C. Maximum likelihood theory