Actuarium

SOA ASTAMAdvanced Short-Term Actuarial Mathematics

Associateship (ASA)
3 hours·6–8 written-answer questions, 60 points·≈400 study hours

Syllabus learning objectives

Official syllabus

Paraphrased from the SOA syllabus so the study-plan builder and practice sets track the topics you will actually be examined on. Weights are the official topic ranges.

Severity, frequency & aggregate models (extreme value, mixtures)

25%
  • Fit and apply mixture distributions and extreme value distributions (GPD, GEV) to model heavy-tailed severity.
  • Compute tail probabilities, VaR and TVaR for fitted severity and aggregate loss distributions.
  • Apply the compound distribution framework with alternative frequency assumptions to catastrophe and liability lines.
  • Assess model risk and parameter uncertainty when extrapolating into the tail of a fitted distribution.

Parametric & Bayesian estimation, credibility

25%
  • Fit loss distributions via maximum likelihood and Bayesian methods, including specification of a prior and derivation of the posterior distribution.
  • Apply Bayesian credibility to combine prior information with observed experience for a hypothetical risk.
  • Compute Bühlmann and empirical Bayes credibility parameters and apply them to a portfolio of risks.
  • Evaluate estimator bias, variance and mean squared error for competing estimation approaches.

Reserving (chain ladder, BF, Mack)

25%
  • Project ultimate losses using chain-ladder, Bornhuetter-Ferguson and Cape Cod methods from loss development triangles.
  • Apply Mack's method to estimate the standard error of chain-ladder reserve estimates.
  • Diagnose triangle anomalies (changes in case reserving, mix shifts) and adjust development factors accordingly.
  • Reconcile paid and incurred development approaches and select a best-estimate reserve.

Pricing, reinsurance & risk measures

25%
  • Price excess-of-loss and aggregate reinsurance treaties using burning cost and exposure rating techniques.
  • Compute risk measures (VaR, TVaR, standard deviation principle) for pricing catastrophe and high-layer covers.
  • Apply increased limit factors and ILFs to price policy limits above a basic limit.
  • Assess the effect of reinsurance structure on ceded premium, retained risk and pricing adequacy.

Lecture videos for this exam

Open the full video library →

[MATH 5639 Actuarial Loss Models] Lecture 1: Probability Exercise 1

Bin Z · Loss Models

[MATH 5639 Actuarial Loss Models] Lecture 17: Ch2.5 Deductible

Bin Z · Loss Models

[MATH 5639 Actuarial Loss Models] Lecture 21: Ch3 Individual Risk Model

Bin Z · Loss Models

[MATH 5639 Actuarial Loss Models] Lecture 41: Ch12.1 Moment and quantile matching methods

Bin Z · Loss Models

Overview

ASTAM is the written-answer short-term exam: advanced loss models including extreme-value distributions, Bayesian and Bühlmann–Straub credibility, stochastic reserving, experience rating, reinsurance and risk measures. Choose ALTAM or ASTAM for ASA.

Duration
3 hours
Questions
6–8 written-answer questions, 60 points
Style
Computer-based written answer
Passing
Scaled 6 of 10

Syllabus map

Severity, frequency & aggregate models (extreme value, mixtures)
25%
Aggregate Loss ModelsExtreme Value Theory and Heavy Tails
Parametric & Bayesian estimation, credibility
25%
Statistics and Estimation for ActuariesCredibility Theory: Limited Fluctuation, Bühlmann, and Bayes
Reserving (chain ladder, BF, Mack)
25%
Reserving Methods: Chain Ladder, Bornhuetter–Ferguson, Benktander, and Cape CodStochastic Reserving: Mack's Model and the ODP Bootstrap
Pricing, reinsurance & risk measures
25%
Ratemaking FundamentalsReinsurance Structures and PricingRisk Measures and Capital

Key formulas

Stop-loss premium   E[(S−d)+]=∑s>d(s−d)P(S=s)\;E[(S-d)_+]=\sum_{s>d}(s-d)P(S=s); recursion   E[(S−d−1)+]=E[(S−d)+]−(1−FS(d))\;E[(S-d-1)_+]=E[(S-d)_+]-(1-F_S(d))

Excess-of-loss reinsurance on X∼Exp(θ)X\sim\text{Exp}(\theta) with retention rr:   E[reinsurer]=θe−r/θ\;E[\text{reinsurer}]=\theta e^{-r/\theta}

Bühlmann–Straub   Zi=mimi+k\;Z_i=\dfrac{m_i}{m_i+k}, μ^\hat\mu = credibility-weighted mean

Generalized Pareto tail   Fˉu(y)=(1+ξy/β)−1/ξ\;\bar F_u(y)=\left(1+\xi y/\beta\right)^{-1/\xi}; Hill estimator   ξ^=1k∑i=1kln⁡X(n−i+1)X(n−k)\;\hat\xi=\dfrac1k\sum_{i=1}^k\ln\dfrac{X_{(n-i+1)}}{X_{(n-k)}}

TVaR   TVaRα=VaRα+E[(X−VaRα)+]1−α\;TVaR_\alpha=VaR_\alpha+\dfrac{E[(X-VaR_\alpha)_+]}{1-\alpha}

Mack process/parameter variance — see CAS Exam 7 guide.

Study strategy

  1. Show all steps: partial credit on ASTAM is generous when the method is right and the arithmetic slips.

  2. Learn the aggregate-loss toolkit (Panjer recursion, normal/lognormal approximations, stop-loss recursion) with small discrete examples.

  3. Practice Mack's formulas on a 4×4 triangle by hand — one full example makes the notation stick.

  4. Be ready to write short explanations of assumptions (why Bühlmann–Straub, why the ODP model).

Common traps

  • Forgetting that a per-payment deductible changes both frequency and severity distributions.

  • Mixing up threshold exceedance (GPD) with block maxima (GEV).

  • Applying E[X∧r]E[X\wedge r] to reinsurer's payment instead of E[X]−E[X∧r]E[X]-E[X\wedge r].

  • Using unweighted average instead of exposure-weighted mean in Bühlmann–Straub.

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