CAS Exam 8 Fall 2013, Question 18
Study guide: Exam 8
An actuary is pricing a Large Dollar Deductible (LDD) workers compensation policy. To price the excess loss portion, an actuary uses a blend of empirical data and a fitted curve to estimate excess loss pure premium factors. The cut-off for empirical data is $250,000. Using the data below, calculate an LDD premium for a policy with a $500,000 deductible and no aggregate limit.
Historical adjusted loss and ALAE for similarly sized risks:
| Loss and ALAE | Observed Percentage Of Claim Counts |
|---|---|
| 8,000 | 80% |
| 100,000 | 11% |
| 250,000 | 6% |
| 500,000 | 2% |
| 1,000,000 | 0.7% |
| 2,000,000 | 0.3% |
Total expected losses per risk = 55,400
Excess ratios based on fitted mixed Exponential-Pareto distribution on losses Truncated and shifted at $250,000:
| Entry Ratio | Excess Ratio |
|---|---|
| 0.1 | 0.92 |
| 0.2 | 0.84 |
| 0.3 | 0.73 |
| 0.4 | 0.69 |
| 0.5 | 0.65 |
| 0.6 | 0.60 |
| 0.7 | 0.55 |
| 0.8 | 0.51 |
| 0.9 | 0.47 |
| 1.0 | 0.44 |
| Item | Value |
|---|---|
| Standard premium | $100,000 |
| Loss based assessment (% of loss and ALAE) | 4% |
| ULAE (% of loss and ALAE) | 8% |
| General expenses (% of standard premium) | 5% |
| Credit risk (% of standard premium) | 5% |
| Acquisition expense (% of net premium) | 8% |
| Tax (% of net premium) | 3% |
| Profit Load (% of net premium) | 5% |
Part a (4 points)
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