CAS Exam 8 Fall 2013, Question 7
Study guide: Exam 8
An actuary is modeling the impact of dispersion on loss development and excess ratios. The actuary has assumed that undeveloped losses are uniformly distributed between $0 and $120,000.
Part a (1 point)
Calculate the excess ratio at $75,000.
Part b (1 point)
Assume a simple dispersion model such that each loss has an equal likelihood of developing by a multiplicative factor of 0.75, 1.00 or 1.25.
Given the following, calculate the excess ratio at $75,000 with simple dispersion.
| Loss | Excess Ratio |
|---|---|
| $50,000 | 0.3403 |
| $56,250 | 0.2822 |
| $60,000 | 0.2500 |
| $93,750 | 0.0479 |
| $100,000 | 0.0278 |
| $110,000 | 0.0069 |
Part c (0.5 points)
Briefly explain two impacts that simple dispersion has on excess ratios.
Answer this question and see the worked solution