CAS Exam 7 Spring 2018, Question 21
Study guide: Exam 9
A company writes two lines of business: personal auto and personal property. An actuary simulated 1,000 loss scenarios of a company's personal property line of business using an Internal Risk Model. Given the following information:
- 1-in-100 TV@R of personal auto = $4.5 million.
- 1-in-100 WTV@R of personal auto = $5 million.
- The company has a total capital of $10 million.
- All scenarios have an equal chance of occurring.
- The actuary calculated the transformed probability function (
F^*(x)) using Wang transform. - The results of the 13 worst scenarios sorted in descending order for personal property:
| Simulation # | Loss | F^*(x) |
|---|---|---|
| 709 | 6,933,000 | 1.000 |
| 330 | 5,606,000 | 0.995 |
| 792 | 4,867,000 | 0.991 |
| 424 | 4,121,000 | 0.987 |
| 114 | 3,022,000 | 0.984 |
| 185 | 2,496,000 | 0.981 |
| 201 | 1,800,000 | 0.978 |
| 977 | 1,293,000 | 0.975 |
| 644 | 1,022,000 | 0.972 |
| 663 | 836,000 | 0.969 |
| 109 | 423,000 | 0.966 |
| 514 | 383,000 | 0.963 |
| 577 | 200,000 | 0.961 |
Part a (0.75 points)
Calculate the allocated capital for each of the lines of business using the proportional allocation method with 1-in-100 TV@R.
Part b (1 point)
Calculate the allocated capital for each of the lines of business using the proportional allocation method with 1-in-100 WTV@R.
Answer this question and see the worked solution