CAS Exam 8 Fall 2013, Question 25
Study guide: Exam 9
An insurance company is considering a sliding-scale commission structure for its niche casualty excess of loss program, comprised of independent retailers. Using the program's loss history, two actuaries are tasked with calculating an aggregate loss distribution.
Given the following information:
- All policies have a $2,000,000 per occurrence insured retention.
- All policies have occurrence limits of either $1,000,000 or $2,000,000 in excess of the insured's retention.
- All policies have a $2,000,000 aggregate limit.
- The only claims that are reported to the insurer are those that exceed the insured's retention.
| Policy Year | Aggregate Loss in Excess of $2,000,000 | Reported Claim Count |
|---|---|---|
| 2000 | - | 0 |
| 2001 | $1,506,002 | 2 |
| 2002 | $1,070,358 | 1 |
| 2003 | - | 0 |
| 2004 | $977,602 | 1 |
| 2005 | $2,490,714 | 2 |
| 2006 | - | 0 |
| 2007 | $512,933 | 1 |
| 2008 | - | 0 |
| 2009 | - | 0 |
Actuary A wants to use the lognormal distribution to determine the aggregate loss distribution. Actuary B prefers Panjer's recursive formula, using a Poisson frequency distribution.
Evaluate each actuary's selection and propose the more appropriate method.
Part a (1.25 points)
Answer this question and see the worked solution
Concepts tested
- Aggregate Loss Model
- Sliding Scale Commissions
- Lognormal Distribution
- Reinsurance Pricing
- Model Selection