CAS Exam 8 Fall 2017, Question 13
Study guide: Exam 8
A risk is written using a balanced retrospective rating plan with the following characteristics:
- Losses at the minimum premium = $50,000
- Losses at the maximum premium = $300,000
- Loss conversion factor = 1.05
- e = $10,000
The following table shows actual experience from a representative sample of risks that are similar to the risk in question:
| Risk | Actual Aggregate Loss | Risk | Actual Aggregate Loss |
|---|---|---|---|
| 1 | $25,000 | 6 | $175,000 |
| 2 | $50,000 | 7 | $200,000 |
| 3 | $100,000 | 8 | $300,000 |
| 4 | $100,000 | 9 | $350,000 |
| 5 | $150,000 | 10 | $550,000 |
Part a (2 points)
Determine the maximum premium that the insured can be charged.
Part b (0.5 points)
An actuary has acquired actual aggregate data from a new book consisting of risks within the same industry. The loss experience of five representative risks from this book is shown below:
| Risk | Actual Aggregate Loss |
|---|---|
| 1 | $275,000 |
| 2 | $300,000 |
| 3 | $500,000 |
| 4 | $700,000 |
| 5 | $800,000 |
The actuary proposes to combine the data from the two books, stating that the combined data will result in a more accurate calculation of the insured's retrospective premium. Assess the validity of the actuary's statement.
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