CAS Exam 8 Fall 2012, Question 17
Study guide: Exam 8
An actuary wants to calculate excess ratios for a book of business based on actual data below $200,000, and from a mix of actual data and a fitted Pareto-exponential curve above $200,000. The following data has been compiled:
| Accident Limit | Observed Excess Ratios by Hazard Group: HG A | HG B | HG C |
|---|---|---|---|
| $50,000 | 0.42 | 0.46 | 0.58 |
| $100,000 | 0.21 | 0.26 | 0.38 |
| $150,000 | 0.11 | 0.16 | 0.26 |
| $200,000 | 0.06 | 0.11 | 0.18 |
| $250,000 | 0.04 | 0.08 | 0.13 |
| $300,000 | 0.03 | 0.06 | 0.10 |
| $500,000 | 0.01 | 0.03 | 0.05 |
| Excess Ratios from Mixed Pareto-Exponential: Entry Ratio | Excess Ratio |
|---|---|
| 0.25 | 0.785 |
| 0.50 | 0.625 |
| 0.75 | 0.500 |
| 1.00 | 0.400 |
| 1.25 | 0.340 |
| 1.50 | 0.290 |
| 1.75 | 0.255 |
| 2.00 | 0.220 |
| Hazard Group | Average Size of Loss Truncated and Shifted to $200,000 |
|---|---|
| HG A | $75,000 |
| HG B | $100,000 |
| HG C | $200,000 |
Part a (1.25 points)
Calculate the excess ratios for the following limits and hazard groups (HG):
- i. HG A; $50,000
- ii. HG B; $300,000
Part b (0.75 points)
Briefly discuss three advantages of using this methodology to generate excess ratios.
Part c (0.5 points)
Discuss whether it would be reasonable to fit a single curve rather than multiple curves by hazard group.
Answer this question and see the worked solution
Concepts tested
- Excess and Deductible Rating
- Workers Compensation Classification
- Retrospective Rating
- Severity Distribution