CAS Exam 8 Fall 2019, Question 1
Study guide: Exam 8
An insurer uses five geographical Storm Zones (A, B, C, D, and E) in their rating plan. The insurer refines their rating plan using the following approach:
- Divide each Storm Zone into numerous geographical sectors.
- For each geographical sector and storm type, calculate the observed storm frequency as number of storms per year.
- There are three storm types defined as Moderate, Strong, and Severe storms.
The insurer performs two credibility procedures to produce estimates of the respective storm frequencies in each sector. The first is a multi-dimensional credibility procedure and the second is a single-dimensional credibility procedure (utilizing only a single storm type).
Part a (1.5 points)
The multi-dimensional credibility results for a particular sector in Storm Zone C for Severe storms are given in the table below. The single-dimensional credibility factor is 0.30.
| Storm Type | Coefficient | Storm Zone Mean Frequency | Sector Mean Frequency |
|---|---|---|---|
| Intercept | not provided | ||
| Moderate | 0.05 | 5.30 | 7.10 |
| Strong | 0.12 | 1.40 | 2.40 |
| Severe | 0.20 | 0.73 | 0.69 |
Calculate the mean frequency estimate of Severe storms for each of the two credibility procedures.
Part b (0.75 points)
Fully explain why the single-dimensional credibility estimate in part a. above is lower than the multi-dimensional credibility estimate.
Answer this question and see the worked solution