Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) Reserving and Pricing for Short-Term Insurance Coverages Practice Questions

Reserving and pricing on SOA Exam ASTAM covers loss development triangles, the chain ladder method, Bornhuetter-Ferguson, Cape Cod method, and generalized linear model (GLM) based ratemaking for P&C insurance.

227 Questions

84 Easy

107 Medium

36 Hard

2026 Syllabus

Sample Questions

Question 1 Easy

Which of the following best describes Allocated Loss Adjustment Expenses (ALAE)?

Solution

B is correct.

Allocated Loss Adjustment Expenses (ALAE) are claim-specific costs that can be directly assigned to an individual claim file, including defense counsel fees, expert witness costs, independent medical exams, and outside adjuster fees retained for that particular claim. Because they are identifiable at the claim level, ALAE is included in the total loss cost used in pure premium calculations.

Question 2 Medium

Which of the following is a core assumption of Mack's model for loss reserving?

Solution

A is correct.

Mack's model (1993) makes three key assumptions:
1.

E[C_{i,k+1} \mid C_{i,1}, \ldots, C_{i,k}] = f_k \cdot C_{i,k}

— the expected cumulative losses at the next age depend only on the current cumulative losses through a proportional relationship.
2.

\text{Var}(C_{i,k+1} \mid C_{i,1}, \ldots, C_{i,k}) = \sigma_k^2 \cdot C_{i,k}

— variance is proportional to current cumulative losses.
3.

\{C_{i,k}\}_{k \geq 1}

are independent across accident years

i

Question 3 Hard

In Mack's (1993) stochastic chain-ladder model, the total reserve MSEP for all accident years combined exceeds the sum of individual accident year MSEPs due to a cross-term from shared development factor estimation. For accident years

i

and

i'

(

i < i'

), the cross-term in the total MSEP is proportional to:

Solution

A is correct.

In Mack (1993), the total MSEP for the aggregate reserve includes cross-terms:

\widehat{\text{MSEP}}(\hat{R}) = \sum_i \widehat{\text{MSEP}}(\hat{R}_i) + 2 \sum_{i < i'} \hat{R}_i \hat{R}_{i'} \sum_{k = n-i'+1}^{n-1} \frac{\hat{\sigma}_k^2}{\hat{f}_k^2 S_k}

The sum over

k

starts at

n - i' + 1

— the first future development interval for the more mature accident year

i'

— and runs to the last interval. This captures the parameter error correlation: both accident years

i

and

i'

will be projected using the same estimated factors

\hat{f}_k

for those future intervals, so their reserve errors are positively correlated.

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Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) Reserving and Pricing for Short-Term Insurance Coverages Practice Questions

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