CAS Exam 7 Spring 2019, Question 10
Study guide: Exam 7
Given the following output from a generalized linear model fitted to a triangle of loss development data as of December 31, 2018:
Standardized Pearson Residuals:
| Accident Year | 12 Months | 24 Months | 36 Months |
|---|---|---|---|
| 2016 | -0.54 | 1.05 | 3.56 |
| 2017 | 1.43 | 2.75 | |
| 2018 | 0.00 |
| Accident Year | Standard Deviation |
|---|---|
| 2016 | 2.067 |
| 2017 | 0.933 |
| Total | 1.570 |
Fitted Cumulative Losses ($000):
| Accident Year | 12 Months | 24 Months | 36 Months |
|---|---|---|---|
| 2016 | 1,250 | 2,000 | 2,150 |
| 2017 | 1,500 | 2,400 | |
| 2018 | 1,400 |
Sample Residual Index (row, column):
| Accident Year | 12 Months | 24 Months | 36 Months |
|---|---|---|---|
| 2016 | (2, 1) | (1, 1) | (2, 1) |
| 2017 | (1, 3) | (2, 2) | |
| 2018 | (1, 2) |
- Assume the residuals in accident years 2017 and 2018 are homoscedastic.
Part a (2 points)
Construct the triangle of sampled cumulative losses based on the above sampling algorithm and adjusting the residuals as necessary.
Part b (1.75 points)
Given the following additional information:
| Cumulative Distribution Function | Expected Losses |
|---|---|
| 20% | 2,500 |
| 60% | 3,000 |
| 100% | 3,500 |
- The tail factor as of 36 months is 1.15.
- 0% loss trend.
- The first stochastically generated random seed for the expected loss is 0.458 and should be applied to the fitted loss triangle.
- The second stochastically generated random seed for the expected loss is 0.812 and should be applied to the sampled loss triangle.
Calculate the range of stochastic Bornhuetter-Ferguson reserve indications.
Answer this question and see the worked solution