CAS Exam 9 Spring 2017, Question 27
Study guide: Exam 9
Two independent, privately held businesses are currently self-insured. The two companies want to pool their risk, which will lower their combined required regulatory capital.
Given the following modeled events:
| Scenario | Probability | Loss for Company A |
|---|---|---|
| 1 | 0.1% | 120,000 |
| 2 | 0.5% | 60,000 |
| 3 | 1.0% | 35,000 |
| 4 | 2.0% | 10,000 |
| 5 | 96.4% | 0 |
| Scenario | Probability | Loss for Company B |
|---|---|---|
| 1 | 0.1% | 100,000 |
| 2 | 0.5% | 25,000 |
| 3 | 1.0% | 10,000 |
| 4 | 2.0% | 2,000 |
| 5 | 96.4% | 0 |
For each company:
- Target Return on Equity: 15%
- Probability of Ruin: 2.5%
Standard deviations of losses:
- Company A: 6,811
- Company B: 3,764
- Combined Losses (A & B): 10,351
Both companies will use the marginal surplus method to allocate risk load.
Calculate and explain the range of capital that Company B can offer for its share of the risk load that will make pooling risk with Company A individually and collectively rational.
Part a (2.5 points)
No current syllabus covers this question; it is kept for the record.
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