SOA Exam ASTAM Spring 2024, Question 5
Study guide: Exam ASTAM
A company sells three classes of policies, A, B, and C, in equal numbers. The per-policy aggregate loss distributions for policies in each class, for one exposure period, are as follows:
| Policy Class | Loss Amount 0 | Loss Amount 100 | Loss Amount 500 |
|---|---|---|---|
| A | 0.90 | 0.07 | 0.03 |
| B | 0.50 | 0.30 | 0.20 |
| C | 0.30 | 0.33 | 0.37 |
Part a (2 points)
Show that the expected value of the hypothetical means is 120 to the nearest 10. You should calculate the value to the nearest 0.1.
Part b (2 points)
Show that the expected value of the process variance, v, is 30,700 to the nearest 100. You should calculate the value to the nearest 1.
Part c (2 points)
Show that the variance of the hypothetical means, a, is 6400 to the nearest 100. You should calculate the value to the nearest 1.
Part d (2 points)
A policy is chosen at random and is observed to have losses of 500 in the first exposure period, 100 in the second exposure period, and 100 in the third exposure period.
Determine the Bühlmann credibility estimate of the net premium for the policy's fourth exposure period.
Part e (2 points)
Calculate the Bayesian estimate of the net premium for the policy's fourth exposure period.
Part f (2 points)
(i) Suppose that v increases while a stays the same. Explain why the resulting change in the Bühlmann credibility factor (that is, increase, decrease, or stay the same) is reasonable.
(ii) Suppose that a increases while v stays the same. Explain why the resulting change in the Bühlmann credibility factor is reasonable.
(iii) Suppose that the number of years of data increases, while a and v remain the same. Explain why the resulting change in the Bühlmann credibility factor is reasonable.
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