CAS Exam 7 Spring 2016, Question 14
Study guide: Exam 7
Given the following output from a generalized linear model fitted to a triangle of loss development data:
Standardized Pearson Residuals:
| Accident Year | 12 Months | 24 Months | 36 Months | 48 Months | 60 Months | 72 Months |
|---|---|---|---|---|---|---|
| 2010 | 1.68 | 2.65 | -4.70 | -2.78 | 3.37 | 0.00 |
| 2011 | 7.74 | -1.34 | -7.33 | -1.91 | -3.61 | |
| 2012 | 5.72 | 1.94 | -6.91 | 4.98 | ||
| 2013 | -1.22 | 0.12 | -1.94 | |||
| 2014 | 1.67 | -1.87 | ||||
| 2015 | 0.00 |
Standard Deviations of Standardized Pearson Residuals:
| Accident Year | Standard Deviation |
|---|---|
| 2010 | 3.571 |
| 2011 | 5.563 |
| 2012 | 5.797 |
| 2013 | 1.045 |
| 2014 | 2.503 |
| Accident Year Range | Standard Deviation |
|---|---|
| 2010 to 2011 | 4.463 |
| 2012 to 2013 | 4.345 |
| 2014 to 2015 | 2.503 |
| 2010 to 2012 | 4.741 |
| 2013 to 2015 | 1.537 |
Fitted Cumulative Losses:
| Accident Year | 12 Months | 24 Months |
|---|---|---|
| 2012 | 3,500 | 7,612 |
| 2013 | 4,210 | 8,749 |
| 2014 | 5,400 | 10,654 |
An actuary reviewing the output notices heteroscedasticity in the residuals. The actuary decides to adjust for this by calculating variance parameters before running the sampling algorithm.
Given the following residual index values from one iteration of the sampling algorithm:
| Accident Year | Sample Residual Index (row, column) |
|---|---|
| 2012 | 5, 1 |
| 2013 | 1, 3 |
| 2014 | 4, 3 |
Part a (2.25 points)
Calculate the actuary's sampled incremental losses for accident years 2012-2014 between 12 and 24 months for the sample under consideration.
Part b (0.5 points)
Explain why heteroscedastic residuals might cause issues when using a bootstrapping technique to estimate variance of unpaid claim estimates.
Answer this question and see the worked solution