Actuarial Notes

SOA Exam ASTAM Sample Question 2

Study guide: Exam ASTAM

Part a

There are four essential objectives of Ratemaking. Describe each one and explain why these objectives are essential.

Part b

You are the rate making actuary for ABC Auto. You are setting rates for the auto coverage, which is a short-term insurance product. You are given the following data:

Calendar Year Earned Premium
2017 10,000
2018 12,000
2019 8,000

Assume that all policies are one-year policies and that policies are issued uniformly throughout the year.

The following rate changes have occurred:

Date Rate Change
March 15, 2017 10% Increase
July 30, 2018 8% Increase
October 31, 2019 4% Decrease
  • (i) Graphically display the parallelogram that would be used to apply the parallelogram method.
  • (ii) Using the parallelogram method, calculate the earned premium for 2017, 2018, and 2019 based on current rates.

Part c

There are two methods for determining the overall change in rates – the loss cost method and the loss ratio method. Prove that both methods will always provide the same answer.

Part d

For collision coverage for ABC Auto, rate differentials for 2019 are developed using the following information:

Type Proportion of Total Drivers Claim Frequency Poisson Annual Severity Gamma
Safe 0.5 0.04 \alpha = 3, \theta = 1000
Not So Safe 0.3 0.10 \alpha = 4, \theta = 1000
Reckless 0.2 0.25 \alpha = 5, \theta = 1000

  • (i) Calculate the indicated differentials for each Type, given that Safe is the base rate.

  • (ii) During 2019, ABC Auto experienced the following loss ratios for collision coverage based on the indicated differentials developed in Question 16 (as printed):

    Type Loss Ratio
    Safe 60%
    Not So Safe 63%
    Reckless 51%

    Use the loss ratio method to determine the new indicated differentials for 2020 for the Not So Safe and Reckless categories.

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