SOA Exam ASTAM Spring 2025, Question 3
Study guide: Exam ASTAM
The ratemaking actuary for a property and casualty insurance company is analyzing automobile claims data.
You are given the following information about the portfolio:
(i) Policies are classified into three classes, A, B, and C, depending on the deductible chosen.
(ii) The annual number of claims per policy within each class is assumed to follow a Poisson distribution, with parameter \lambda varying across classes.
(iii) The ground-up loss severity for all classes is assumed to follow a Pareto distribution with \alpha = 2 and \theta = 2500.
(iv) Claim frequency and loss severity are independent.
(v) The current differentials are based on expected aggregate claim amount.
(vi) The table below shows the claim frequency information for the different classes.
| Class | Deductible | Claim Frequency Poisson, \lambda |
|---|---|---|
| A (Base Rate) | 500 | 0.0625 |
| B | 1000 | 0.0510 |
| C | 1500 | 0.0430 |
Part a (1 point)
State two considerations regarding the data to use for determining deductible relativities.
Part b (3 points)
(i) Show that the expected aggregate claim amount for a Class A policy is 190 to the nearest 10. You should calculate the value to the nearest 0.1.
(ii) Calculate the current differential for Class B.
(iii) Calculate the current differential for Class C.
Part c (3 points)
The current differentials are updated using the experience shown in the following table:
| Class | Claims | Earned Exposure |
|---|---|---|
| A (Base Rate) | 3,465,000 | 18,500 |
| B | 1,335,000 | 8,000 |
| C | 350,000 | 2,200 |
(i) Calculate the new indicated differential for Class B using the loss cost method.
(ii) Calculate the new indicated differential for Class C using the loss cost method.
(iii) Show that the off-balance factor using the new indicated differentials is 0.98 to the nearest 0.01. You should calculate the value to the nearest 0.001.
Part d (3 points)
The current base rate for Class A is 200. The insurer decides to implement an overall rate increase of 10%.
(i) Show that the resulting percentage increase in the base rate is between 12% and 13%. You should calculate the value to the nearest 0.1%.
(ii) Show that the percentage increase in premium for Class C policies is between 4% and 5%. You should calculate the value to the nearest 0.1%.
(iii) The marketing manager suggests instead applying a uniform 10% increase to the premiums of all classes. Critique this suggestion.
Answer this question and see the worked solution
Concepts tested
- Classification Ratemaking
- Balancing Back
- Loss Cost
- Deductible
- Pareto Distribution
- Overall Rate Level Indication