CAS Exam 7 Spring 2017, Question 23
Study guide: Exam 9
A multiline insurance company is considering different reinsurance options. The following table contains the cumulative probability distributions for net premium minus net losses under three scenarios: BARE (no reinsurance), the current reinsurance structure, and the alternative reinsurance structure.
| Probability | BARE | Current | Alternative |
|---|---|---|---|
| 0.00% | -217,911,928 | -196,110,272 | -154,691,590 |
| 0.25% | -71,606,742 | -53,319,764 | -52,785,091 |
| 0.50% | -50,326,877 | -31,517,432 | -26,643,103 |
| 1.00% | -31,241,388 | -14,127,673 | -11,094,195 |
| 2.00% | -17,530,205 | -5,375,766 | -6,715,733 |
| 4.00% | -8,476,413 | -2,672,775 | -4,229,923 |
| 8.00% | -2,252,408 | -1,431,366 | -2,746,629 |
| 10.00% | -559,293 | -1,084,345 | -2,028,415 |
| 20.00% | 3,431,549 | 1,100,974 | 1,980,256 |
| 25.00% | 4,197,741 | 1,929,228 | 2,993,689 |
| 50.00% | 5,519,858 | 3,043,212 | 4,453,299 |
The following table shows the ceded premium and expected recoveries under each reinsurance structure after reinstatement:
| Ceded Premium | Expected Recoveries | |
|---|---|---|
| Current | 4,307,000 | 2,632,000 |
| Alternative | 2,700,000 | 1,676,000 |
Part a (1.75 points)
Construct a cost/benefit diagram at each of the following return periods:
- i. 1-in-10 years
- ii. 1-in-25 years
- iii. 1-in-100 years
- iv. 1-in-200 years
Part b (0.75 points)
Recommend a reinsurance structure for the company to implement utilizing the results in part a. above.
Part c (0.25 points)
The model that produced the loss distributions above used a Frank copula for correlating lines of business for clash and accumulation events. Briefly describe a possible improvement to the model.
Answer this question and see the worked solution