Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) Lessons

All 25 SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lessons are free to read, each with worked examples and audio narration. No signup required.

Severity Models

• Describe how changes in the parameters affect the distributions. (8 min)
• Create new distributions by multiplication by a constant, raising to a power, exponentiation, mixing and splicing. (26 min)
• Understand and interpret the characteristics of severity distributions. (7 min)
• Compare two distributions based on various characteristics of their tails, including moments, ratios of moments, limiting tail behavior, hazard rate functions, and mean excess functions. (24 min)
• Understand the derivation and characteristics of the Generalized Extreme Value and the Generalized Pareto distributions. (10 min)
• Apply the Generalized Extreme Value and the Generalized Pareto distributions to the estimation of tail risk measures and probabilities. (25 min)

Aggregate Models

• Use convolution and recursive formulas to derive probability and distribution functions for aggregate claims distributions with (a,b,0) or (a,b,1) frequency, and with discrete severity distributions. (28 min)
• Derive the discretized version of a continuous distribution using the method of rounding and local moment matching. (15 min)
• Perform calculations for sums of compound Poisson models. (26 min)

Coverage Modifications

• Evaluate the effects of the following coverage modifications: deductibles, policy limits, maximum covered loss, coinsurance, and stop loss reinsurance. (31 min)
• Calculate and interpret loss elimination ratios, increased limits factors, and deductible factors. (12 min)
• Evaluate and interpret the effects of inflation on losses. (11 min)

Construction and Selection of Parametric Models

• Estimate the parameters for frequency and severity distributions by maximum likelihood. (31 min)
• Estimate the variance of the estimators and construct normal and non-normal confidence intervals. (19 min)
• Use the delta method to estimate the variance of the maximum likelihood estimator of a function of the parameter(s). (20 min)
• Estimate the parameters for severity, frequency, and aggregate distributions using Bayesian Estimation. (9 min)
• Perform model selection using graphical procedures, hypothesis tests (Kolmogorov-Smirnov, Chi-square goodness-of-fit, Likelihood ratio), and score-based approaches (SBC, BIC, AIC). (35 min)

Credibility

• Explain and apply Bayesian (greatest accuracy) credibility. (11 min)
• Apply Buhlmann and Buhlmann-Straub models and understand their relationship to Bayesian models. (36 min)
• Explain and apply empirical Bayesian estimation in the nonparametric and semiparametric cases. (13 min)

Reserving and Pricing for Short-Term Insurance Coverages

• Understand, interpret, and apply techniques for estimating outstanding claims, using Expected Loss Ratio, Chain-Ladder, Bornhuetter-Ferguson, Bayesian, and Frequency and Severity methods. (32 min)
• Understand, interpret, and apply the following statistical models and assumptions used for outstanding claims reserves: Mack's model, Poisson model, and Overdispersed Poisson model. (11 min)
• Calculate projected losses using trend analysis. (11 min)
• Calculate overall average rates and rate changes using the loss cost and loss ratio methods. (33 min)
• Calculate risk classification differential changes, including balancing back. (10 min)