ASA exams

ASTAM

Advanced Short-Term Actuarial Mathematics

5 discussions

Study strategy

ASTAM: Written explanations should identify the assumption being tested

For applied work, “the result is reasonable” is not enough. State which diagnostic or assumption supports that judgment. A short answer can be specific without reciting every formula on the syllabus.

Worked example or practice scenario

Suppose a reserve estimate falls while claim counts rise. A useful check separates frequency, average severity, payment timing and case-reserve practice. Merely saying that more claims imply a higher reserve misses the timing and size of those claims.

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Practise a three-part explanation: observation, possible mechanism, check that could distinguish it from another mechanism. Match your practice format to the current official instructions and sample materials. Do not share or seek confidential assessment content.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

ASTAM: Development and BF react differently to immature experience

Development methods extrapolate observed claims using a pattern. BF combines observed claims with expected unreported or unpaid claims. The reported fraction and expected ultimate assumption must refer to the same data basis.

Worked example or practice scenario

Expected ultimate claims are 1,000 and only 25% are expected reported. Actual reported claims are 300. Development ultimate is 300/.25=1,200; BF ultimate is 300+1,000×.75=1,050. These methods use current experience differently.

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Change reported claims to 200 and compare results. Then vary the expected ultimate assumption. A method comparison is not a vote: explain which data or assumption each method relies on and why one might be more stable at the selected maturity.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

ASTAM: Compound totals reveal which variance assumption you used

The variability of a total comes from severity and frequency. Write the conditional expectation and variance first; then use total expectation and total variance. This makes the assumptions visible and helps avoid mixing compound Poisson and fixed-count results.

Worked example or practice scenario

A Poisson count with mean 4 and independent exponential severities with mean 200 gives E[S]=800. Severity second moment is 80,000, so Var(S)=4×80,000=320,000. The standard deviation is about 565.69.

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Compare with exactly four severities: the variance would be 160,000. Now consider a negative-binomial frequency with variance larger than its mean. Explain which term grows before using any numerical approximation.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

ASTAM: Credibility is a model for within- and between-risk variation

Bühlmann credibility balances observed experience against a collective mean. EPV captures process variation within a risk; VHM captures variation in risk means. A large sample alone does not establish credibility without those components and model assumptions.

Worked example or practice scenario

For n=4 observations, EPV=100 and VHM=25, K=4 and Z=n/(n+K)=.5. If the risk mean is 120 and the collective mean is 100, the credibility estimate is 110.

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Double n and compute Z=8/12, giving 113.33. Explain why larger VHM would increase credibility with EPV fixed: the risks are more heterogeneous, so the risk’s own experience is more informative.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

ASTAM: Limited expected values measure the layer you actually pay

A limit and a deductible operate on the loss variable in different ways. Define the insurer payment explicitly. For an ordinary deductible d and payment limit u, Y=min((X−d)+,u), not min(X,u)−d in every case.

Worked example or practice scenario

For an exponential loss with mean 1,000, E[min(X,500)]=1,000(1−e^−.5)≈393.47. With deductible 200 and payment limit 500, expected payment is 1,000(e^−.2−e^−.7)≈322.15.

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Sketch the payment function across X<200, 200<X<700 and X>700. Use the survival-function integral to verify the expectation. Confirm whether a stated policy limit is a ground-up loss limit or a maximum insurer payment.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1