SOA Exam ASTAM Fall 2023, Question 6
Study guide: Exam ASTAM
You are analyzing the following cumulative claims run-off triangle information using Mack's model. Assume all claims are settled by the end of Development Year (DY) 4.
Accident Year (AY) i |
DY 0 | DY 1 | DY 2 | DY 3 | DY 4 |
|---|---|---|---|---|---|
| 0 | 2296 | 2846 | 3120 | 3284 | 3336 |
| 1 | 2183 | 3001 | 3263 | 3471 | |
| 2 | 2201 | 2797 | 3197 | ||
| 3 | 2226 | 2561 | |||
| 4 | 2456 | ||||
\hat{f}_j |
1.2581 | ? | 1.0583 | 1.0158 | |
\hat{\sigma}_j |
4.3438 | ? | 0.4465 | 0.1248 | |
S_j |
8906 | 8644 | 6383 | 3284 |
Part a (1 point)
Show that \hat{f}_1 = 1.1 to the nearest 0.1. You should calculate the value to the nearest 0.01.
Part b (2 points)
Show that the estimated total claims cost for AY 3 is \hat{C}_{3,4} = 3050 to the nearest 10. You should calculate the value to the nearest 0.1.
Part c (2 points)
Show that \hat{\sigma}_1 = 1.6 to the nearest 0.1. You should calculate the value to the nearest 0.01.
Part d (3 points)
- (i) Show that the process standard deviation for outstanding claims for AY 3, using Mack's approximation, is 90 to the nearest 10. You should calculate the value to the nearest 0.1.
- (ii) Calculate the square root of the estimation error for AY 3 using Mack's approximation.
- (iii) Explain the difference between the variability described by the process variance and the variability described by the estimation error.
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