CAS Exam 8 Fall 2017, Question 18
Study guide: Exam 9
A homogenous group of property risks exhibit the following risk profile:
| Exposure Distribution | Losses as a percent of the Maximum Possible Loss (MPL) |
|---|---|
| 80% | 0% |
| 6% | 25% |
| 8% | 50% |
| 4% | 75% |
| 2% | 100% |
Part a (2 points)
Plot the exposure curve, G(x). Label the axes and the points on the curve.
Part b (0.75 points)
Determine the parameters b and g for the 2 parameter MBBEFD distribution that fits this exposure curve using the following information:
Calculated value of parameter b
Parameter g |
\mu = 40.0% |
42.5% | 45.0% | 47.5% | 50.0% | 52.5% | 55.0% | 57.5% | 60.0% |
|---|---|---|---|---|---|---|---|---|---|
| 50.0 | 0.0023 | 0.0017 | 0.0013 | 0.0009 | 0.0005 | 0.0003 | 0.0002 | 0.0001 | 0.0001 |
| 25.0 | 0.0096 | 0.0073 | 0.0055 | 0.0041 | 0.0022 | 0.0015 | 0.0010 | 0.0006 | 0.0004 |
| 16.7 | 0.0239 | 0.0181 | 0.0137 | 0.0103 | 0.0057 | 0.0039 | 0.0026 | 0.0017 | 0.0010 |
| 12.5 | 0.0483 | 0.0365 | 0.0276 | 0.0209 | 0.0118 | 0.0081 | 0.0055 | 0.0036 | 0.0023 |
| 10.0 | 0.0877 | 0.0659 | 0.0497 | 0.0375 | 0.0212 | 0.0147 | 0.0100 | 0.0067 | 0.0044 |
| 8.3 | 0.1498 | 0.1116 | 0.0836 | 0.0628 | 0.0354 | 0.0245 | 0.0168 | 0.0113 | 0.0075 |
| 7.1 | 0.2470 | 0.1817 | 0.1347 | 0.1004 | 0.0561 | 0.0389 | 0.0267 | 0.0181 | 0.0121 |
| 6.3 | 0.4000 | 0.2892 | 0.2116 | 0.1561 | 0.0861 | 0.0594 | 0.0408 | 0.0277 | 0.0185 |
| 5.6 | 0.6446 | 0.4557 | 0.3277 | 0.2385 | 0.1291 | 0.0885 | 0.0605 | 0.0411 | 0.0276 |
| 5.0 | 1.0469 | 0.7190 | 0.5055 | 0.3616 | 0.1910 | 0.1297 | 0.0882 | 0.0597 | 0.0400 |
Part c (0.5 points)
A reinsurer uses this exposure curve to price a property excess of loss treaty where the underlying limit is $100 million. Calculate the proportion of total losses in the layer $25 million excess of $25 million.
Answer this question and see the worked solution