CAS Exam 7 Spring 2018, Question 10
Study guide: Exam 7
Given the following information as of December 31, 2017:
Incremental Paid Loss ($000) as of (months):
| Accident Year | 12 | 24 |
|---|---|---|
| 2013 | 600 | 1,300 |
| 2014 | 650 | 1,400 |
| 2015 | 550 | 1,400 |
| 2016 | 700 | 1,450 |
| 2017 | 700 |
- Exposures are stable over the years.
- There are no calendar or accident date trends in the data.
- A simple linear regression
y = a + bxof the incremental loss at age 24 over the cumulative loss at age 12 was performed. The resulting regression coefficients are:a = 1{,}075b = 0.5
- For a simple linear regression
y = a + bx, the standard error for the slope (b) and intercept (a) are calculated as:
s_b = \sqrt{\sum_i \frac{\epsilon_i^2}{(n - 2) \sum_i (x_i - \bar{x})^2}}
s_a = s_b \sqrt{\frac{1}{n} \sum_i x_i^2}
where \epsilon_i are the error terms.
Part a (2 points)
Test for significance of the 12-24 loss development factor and state the chain ladder model assumption that this test is used to validate.
Part b (0.5 points)
Discuss how the estimated future loss emergence for a year with abnormally high losses to date would differ under the chain ladder versus additive model.
Answer this question and see the worked solution