CAS Exam 8 Fall 2014, Question 14
Study guide: Exam 8
An actuary is pricing an excess workers compensation policy with the following characteristics:
- Excess loss pure premium factors are based on empirical data for losses and ALAE up to $250,000 and a fitted curve for losses greater than $250,000
- $1,000,000 attachment point
- No aggregate limit
Historical adjusted data for similarly sized risks:
| Loss Amount | Probability |
|---|---|
| $20,000 | 70% |
| 100,000 | 14% |
| 250,000 | 8% |
| 500,000 | 5% |
| 750,000 | 2% |
| 1,000,000 | 1% |
| Item | Value |
|---|---|
| Standard Premium | $500,000 |
| ULAE as Ratio of Loss+ALAE | 6.0% |
| General Expense | 2.0% |
| Acquisition Expense | 5.0% |
| Tax | 3.0% |
| Profit and Contingency Margin | -10.0% |
- Empirical data has been truncated and shifted at $250,000 and normalized to a unity mean.
- A mixed Exponential-Pareto curve has been fit to the resulting mean residual lives as described by the following parameters:
| Distribution | Pareto | Exponential |
|---|---|---|
| Cumulative Function | 1 - \left(1 + \frac{x}{b}\right)^{-s} |
1 - e^{-x/c} |
| Mean | \frac{b}{s-1} |
c |
| Variance | \frac{b^2 s}{(s-1)^2 (s-2)} |
c^2 |
| Excess Ratio | \left(1 + \frac{x}{b}\right)^{1-s} |
e^{-x/c} |
| Mean Residual Life | \frac{b + x}{s - 1} |
c |
| Shape | 4.0 | n/a |
| Scale | 12.0 | 0.8 |
| Weight | 0.050 | 0.950 |
Calculate the premium for this policy.
Part a (3.75 points)
Answer this question and see the worked solution