CAS Exam 8 Fall 2015, Question 10
Study guide: Exam 8
One common expression for the experience modification for a single-split plan is:
M = 1 + Z_p \frac{A_p - E_p}{E} + Z_e \frac{A_e - E_e}{E}
where:
Mis the modification factorZ_pandZ_eare credibility constantsA_pis the actual primary lossA_eis the actual excess lossE_pis the expected primary lossE_eis the expected excess lossEis the expected total loss.
Part a (0.75 points)
In the right-hand side of the equation above, there are three terms separated by '+' signs. Briefly describe the role that each term serves in computing the experience mod.
Part b (0.5 points)
Of the two credibility constants, Z_p and Z_e, identify which of the two is typically the larger in magnitude, and explain why.
Part c (1.75 points)
Determine the effectiveness of each of the following credibility functions and select which function is the most appropriate.
| Expected Loss | Credibility: Function 1 | Function 2 | Function 3 | Function 4 |
|---|---|---|---|---|
| 1,000 | 15% | 65% | 55% | 80% |
| 2,000 | 35% | 75% | 63% | 75% |
| 3,000 | 55% | 85% | 70% | 62% |
| 4,000 | 75% | 95% | 76% | 53% |
| 5,000 | 95% | 105% | 81% | 40% |
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