Exam ASTAM – Advanced Short-Term Actuarial Mathematics

6 个单元 · 25 个章节

免费 Exam ASTAM – Advanced Short-Term Actuarial Mathematics 学习笔记，适合 SOA (Society of Actuaries) 学生。每个章节都覆盖一个重点主题，并附例题与可延伸到 thinka app 的练习提示。

Severity Models

Effects of parameters on distributions
Creating new distributions: multiplication, powers, exponentiation, mixing, and splicing
Characteristics of severity distributions
Comparing distribution tails
Generalized Extreme Value and Generalized Pareto distributions
Applying GEV and GPD to tail risk estimation

Aggregate Models

Convolution and recursive formulas for aggregate claims
Discretizing continuous distributions: rounding and local moment matching
Sums of compound Poisson models

Coverage Modifications

Effects of coverage modifications: deductibles, limits, coinsurance, and stop loss
Loss elimination ratios, increased limits factors, and deductible factors
Effects of inflation on losses

Construction and Selection of Parametric Models

Maximum likelihood estimation for frequency and severity distributions
Variance of estimators and confidence intervals
The delta method
Bayesian estimation
Model selection: graphical procedures, hypothesis tests, and score-based criteria

Credibility

Bayesian (greatest accuracy) credibility
Bühlmann and Bühlmann-Straub models
Empirical Bayesian estimation: nonparametric and semiparametric cases

Reserving and Pricing for Short-Term Insurance Coverages

Estimating outstanding claims: Expected Loss Ratio, Chain-Ladder, Bornhuetter-Ferguson, Bayesian, and Frequency-Severity
Statistical reserving models: Mack's, Poisson, and Overdispersed Poisson
Projected losses using trend analysis
Overall average rates and rate changes: loss cost and loss ratio methods
Risk classification differential changes, including balancing back

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