CAS Exam 8 Fall 2016, Question 17
Study guide: Exam 8
The following table contains historical adjusted Worker's Compensation loss experience:
| Loss Size | Number of Claims |
|---|---|
| <$100,000 | 62 |
| $100,000 | 23 |
| $200,000 | 7 |
| $300,000 | 5 |
| $500,000 | 2 |
| $1,000,000 | 1 |
Mean claim size for losses less than $100,000: $38,000.
Excess ratios were calculated directly from data for limits of $100,000 or less. For higher limits a mixed Pareto-Exponential curve was fit to losses truncated and shifted at $100,000, then normalized to mean unity. Selected values of the fitted curve of these excess ratios are shown in the table below.
| Entry Ratio | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.1 | 1.2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Excess Ratio | 0.92 | 0.83 | 0.76 | 0.69 | 0.63 | 0.58 | 0.53 | 0.49 | 0.45 | 0.41 | 0.38 | 0.35 |
Part a (1.5 points)
Calculate an excess ratio for a limit of $250,000.
Part b (1 point)
An actuary is pricing for Excess Worker's Compensation Coverage. Evaluate the impact to the excess premium under the following alternative methodologies:
- Changing the selected truncation point from $100,000 to $300,000.
- Fitting losses using a Pareto Curve.
Answer this question and see the worked solution