CAS Exam 9 Spring 2018, Question 19
Study guide: Exam 9
An insurance company writes two lines of business. The company has recently decided to purchase reinsurance on Line B while continuing to assume all the risk on Line A. Given the following:
- Company management has a target surplus of 1.2 times the average negative income in the cases where it is below the 1% level.
- Company surplus = 8,000,000.
- Mean investment income on surplus = 350,000.
- Mean underwriting result for line A = 475,000.
- Mean underwriting result for line B = 375,000.
- Line B net cost of reinsurance = 125,000.
The last five columns give the Mean Value of TVAR:
| % | Income is Below | Total | Line A | Line B | Investment | Reinsurance |
|---|---|---|---|---|---|---|
| 0.1 | (6,200,238) | (6,278,992) | (2,172,504) | (4,990,202) | (762,087) | 1,645,800 |
| 0.2 | (5,555,683) | (5,794,174) | (2,017,695) | (4,550,118) | (727,019) | 1,500,658 |
| 0.4 | (4,897,611) | (5,329,696) | (1,871,014) | (4,058,038) | (739,011) | 1,338,367 |
| 1.0 | (4,008,814) | (4,562,868) | (1,652,339) | (3,435,305) | (608,209) | 1,132,986 |
| 2.0 | (3,300,000) | (3,996,893) | (1,450,891) | (2,954,906) | (565,643) | 974,547 |
| 5.0 | (2,307,688) | (3,142,100) | (1,133,566) | (2,305,593) | (463,340) | 760,399 |
| 10.0 | (1,494,462) | (2,361,762) | (857,697) | (1,804,880) | (294,446) | 595,261 |
Part a (1.75 points)
Determine the mean return on allocated surplus net of reinsurance for Line B.
Part b (0.5 points)
After purchasing reinsurance on Line B the company re-evaluates its surplus position. Determine the amount of total surplus the company could release.
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