CAS Exam 8 Fall 2019, Question 17
Study guide: Exam 9
An insurer is deciding on a proportional reinsurance strategy for the upcoming two years. A reinsurer proposes the following sliding-scale commission with a carry-forward provision. The contract will be identical for the second year.
| Minimum Commission: | 12.5% at an 80% loss ratio |
|---|---|
| Sliding 1:1 to | 27.5% at a 65% loss ratio |
| Sliding .5:1 to a Maximum | 35% at a 50% loss ratio |
Assume the insurer places no value on the carry-forward provision after the second year, and ignore the time value of money (i.e., assume a 0% interest rate).
The following table details the expected loss distribution of the underlying business:
| Range of Loss Ratios | Average Loss Ratio in Range | Probability of Being in Range |
|---|---|---|
| 0% - 50% | 43% | 0.15 |
| 50% - 60% | 57% | 0.25 |
| 60% - 80% | 68% | 0.45 |
| 80% or above | 85% | 0.15 |
Calculate the reinsurer's expected technical ratio for each year if the insurer buys the sliding-scale commission contract for both years.
Part a (3 points)
Answer this question and see the worked solution