CAS Exam 7 Spring 2019, Question 6
Study guide: Exam 7
Given the following information as of December 31, 2018:
| Accident Year | On-Level Earned Premium ($000,000) | Cumulative Paid Loss at 12 Months ($000,000) | Cumulative Paid Loss at 24 Months ($000,000) | Cumulative Paid Loss at 36 Months ($000,000) |
|---|---|---|---|---|
| 2016 | 13,000 | 360 | 1,425 | 2,850 |
| 2017 | 13,250 | 375 | 1,375 | |
| 2018 | 13,500 | 350 |
- The expected loss payment pattern follows a loglogistic curve of the form
\frac{x^{\omega}}{x^{\omega} + \theta^{\omega}}, where\omega = 1.448\theta = 48.021
- There are no payments after 120 months.
- Accidents occur uniformly throughout the year.
- The scale parameter,
\sigma^2, is 423.
Part a (1.75 points)
Calculate the incremental fitted payment and corresponding normalized residual for accident year 2018 at 12 months using the Cape Cod method.
Part b (0.75 points)
Calculate ultimate losses for accident year 2016 using the Cape Cod method.
Answer this question and see the worked solution