CAS Exam 8 Fall 2016, Question 21
Study guide: Exam 9
An insurance company insures high value homes and plans to increase the maximum property value they will insure next year. The company is considering purchasing a new $4,000,000 excess of $4,000,000 reinsurance treaty. The reinsurer is given the following limit profile:
| Insured Value Range | Experience Period On-Level Premium | Treaty Subject Premium |
|---|---|---|
| $1,000,000 to $4,000,000 | $100,000,000 | $25,000,000 |
| $4,000,001 to $8,000,000 | $0 | $5,000,000 |
A reinsurance actuary has trended and developed the portfolio's historical losses for the Experience Period:
| Loss Size | Number of Claims | Experience Period Ground-up Loss |
|---|---|---|
| Less than $1,000,000 | 200 | $22,000,000 |
| Greater than $1,000,000 | 10 | $18,000,000 |
| Total | 210 | $40,000,000 |
The actuary is unsure if a Swiss Re Y_3 or Y_4 exposure curve is a better fit. The following MBBEFD exposure curve formulas are available along with the following information:
G(x) = \frac{\ln\left[\dfrac{(g-1)b + (1-gb)b^x}{1-b}\right]}{\ln(gb)}
b(c) = e^{3.1 - .15c(1+c)} \qquad g(c) = e^{c(.78 + .12c)}
| % of Insured Value | % of Cumulative Loss, Y_3 |
Y_4 |
|---|---|---|
| 25% | 60% | 73% |
| 40% | 72% | 82% |
| 100% | 100% | 100% |
Given a proposed treaty rate of 1% of total subject premium, calculate the expected ceded loss ratio for the new treaty.
Part a (4 points)
Answer this question and see the worked solution