Sample Questions
Question 1
Easy
The reported development (chain ladder) technique relies most directly on which key assumption?
Solution
C is correct. The development technique projects ultimate losses by multiplying losses reported (or paid) to date by an age-to-ultimate factor derived from historical emergence patterns. This works only if the amounts reported to date are predictive of future development and that emergence pattern is stable across accident years.
Question 2
Medium
Cumulative paid losses (in thousands) are shown below.
| Accident Year | 12 months | 24 months |
|---|---|---|
| 2022 | 1,600 | 2,000 |
| 2023 | 2,400 | 3,120 |
Using the volume-weighted (all-year) average, what is the selected 12-to-24 month age-to-age factor?
| Accident Year | 12 months | 24 months |
|---|---|---|
| 2022 | 1,600 | 2,000 |
| 2023 | 2,400 | 3,120 |
Using the volume-weighted (all-year) average, what is the selected 12-to-24 month age-to-age factor?
Solution
E is correct. The volume-weighted factor divides the sum of the later cumulative values by the sum of the earlier cumulative values across all years: . This weights each accident year by its loss volume rather than treating the two individual factors (1.25 and 1.30) equally.
Question 3
Hard
An actuary estimates ultimate losses for a long-tailed line using the Benktander (Gunnar-Benktander) method. Earned premium is $16,000,000 with an expected loss ratio of 62.5%. Age-to-age factors are 12-to-24 = 1.25 and 24-to-36 = 1.60 with a tail of 1.00, and reported losses at 12 months are $6,000,000. What is the Benktander ultimate loss estimate?
Solution
E is correct. Expected losses are . The CDF to ultimate at 12 months is , so the reported percentage is and the unreported percentage is 0.50. The BF ultimate is . Benktander uses the BF ultimate as the revised a priori: .
