CAS Exam 8 Fall 2019, Question 15
Study guide: Exam 8
An actuary is pricing a retrospectively rated policy with a per occurrence limit of 20,000 and no minimum or maximum ratable loss.
Using claim data from a group of similar policies, the actuary fit the following regression line to the excess severity to estimate losses using the shifted Pareto distribution. The fitted regression function is y = 0.4467x + 16112 with R^2 = 0.9826.
Given the following:
| Included in: | ||
|---|---|---|
| Loss adjustment expenses as a percentage of loss | 10% | Loss conversion factor |
| Commission as a percentage of retrospective premium | 9% | Tax multiplier |
| Premium tax as a percentage of retrospective premium | 8% | Tax multiplier |
| Fixed overhead expenses | 50,000 | Basic premium |
| Underwriting profit as a percentage of expected excess loss | 6% | Basic premium |
- The number of claims for ground up losses is Poisson distributed with
\lambda = 15.
Part a (2 points)
Calculate the basic premium.
Part b (1 point)
Assuming that actual limited losses equal half the expected limited losses, calculate the retrospective premium.
Part c (0.5 points)
Assess the actuary's decision to use the shifted Pareto distribution to estimate excess severity.
Answer this question and see the worked solution