CAS Exam 7 Spring 2013, Question 5
Study guide: Exam 7
Given the following information as of December 31, 2012:
| Accident Year | Cumulative Reported Loss 12 ($000) | Cumulative Reported Loss 24 ($000) | Cumulative Reported Loss 36 ($000) | Cumulative Reported Loss 48 ($000) |
|---|---|---|---|---|
| 2009 | 233 | 522 | 570 | 601 |
| 2010 | 204 | 480 | 512 | |
| 2011 | 242 | 541 | ||
| 2012 | 255 |
- Claim data in the triangle is on an unlimited basis
- Basic limit: $50,000
- Calendar period ground-up unlimited loss trend: 5% per year
- An exponential distribution fit to the claim level data at each maturity produced the following unlimited claim size means at the accident year 2012 level:
| 12 | 24 | 36 | 48 | |
|---|---|---|---|---|
| Unlimited Claim Size Mean | 26,000 | 48,000 | 58,000 | 66,000 |
- Mean of exponential distribution:
\theta - Variance of exponential distribution:
\theta^2 - Limited mean of exponential distribution at limit
k:\theta\left(1 - e^{\frac{k}{\theta}}\right)
Using the method described by Sahasrabuddhe, calculate the latest diagonal of the cumulative reported loss triangle based on accident year 2012 cost levels for the basic limit of loss.
Part a (2.25 points)
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