SOA Exam ASTAM Spring 2024, Question 2

XYZ Insurance sells medical liability insurance.

Part a (1 point)

Briefly describe two differences between the distributions of the loss for a single policy and the average loss per policy for a large portfolio of independent policies.

Part b (2 points)

You are the ratemaking actuary for XYZ Insurance. XYZ uses the following data to determine the indicated premium rate on its medical liability insurance:

Item	Value
Expected Effective Period Incurred Losses (000s)	25,000
Fixed Expenses (000s)	3,000
Earned Exposure Units (000s)	20
Permissible Loss Ratio	0.85

Show that the indicated premium rate is 1,650 to the nearest 10. You should calculate the value to the nearest 1.

Part c (1 point)

XYZ sells medical insurance in Regions A, B, and C. XYZ used the following differentials and had the following experience:

Region	Existing Differential	Experience Period Loss Ratio at Current Rates	Exposure Units (000s)
A	0.80	0.72	5
B	1.00	0.80	10
C	1.20	0.76	5

Determine the indicated differential for each region using the loss ratio method.

Part d (2 points)

Another method for calculating new differentials is the loss cost method.

(i) Explain one reason why the differentials calculated by the two methods might produce different results.

(ii) Explain what conditions are required for the two methods to produce the same results.

Part e (2 points)

You are given the following additional data:

Item	Value
Base Premium Rate for Region B	1,500
Target Premium Increase	9.8%

Calculate the revised base premium rate such that the premium change and the differentials are balanced.

Answer this question and see the worked solution