Sample Questions
Question 1
Easy
In estimating unpaid claims with the development (chain-ladder) technique, what does a tail factor represent?
Solution
C is correct. A tail factor extends development beyond the oldest maturity observed in the triangle out to ultimate, capturing the loss emergence that occurs after the latest available data point. Triangles are finite, so the tail factor accounts for development the observed link ratios cannot measure.
Question 2
Medium
An actuary subdivides a book of business into segments before estimating unpaid claims. In this context, a segment is described as 'credible' when it:
Solution
C is correct. Credibility refers to whether a segment contains enough claim volume and experience to yield statistically stable, reliable estimates. Grouping claims into homogeneous segments improves the relevance of development patterns, but each segment must still be large enough that random fluctuation does not dominate the observed factors. This is the central tension: finer segmentation raises homogeneity but can leave individual cells too thin to be credible.
Question 3
Hard
While vetting a claim-count reserve analysis, an actuary reconciles the following figures for accident year 2019 at the latest evaluation:
| Metric | Count |
|---|---|
| Reported claims | 1,050 |
| Closed claims | 1,080 |
| Selected ultimate claims | 1,040 |
Applying a reasonableness check, what should the actuary conclude?
| Metric | Count |
|---|---|
| Reported claims | 1,050 |
| Closed claims | 1,080 |
| Selected ultimate claims | 1,040 |
Applying a reasonableness check, what should the actuary conclude?
Solution
D is correct. A basic reasonableness check on claim counts is that reported ≥ closed, because a claim must be reported before it can be closed, and that ultimate ≥ reported for an immature or mature year. Here closed claims (1,080) exceed reported claims (1,050), and selected ultimate (1,040) is below both. These relationships are internally impossible, so the figures signal a data or reconciliation error—such as duplicate closed transactions or a mismatched extract—that must be corrected before any estimate is trusted.
