IAI Actuarial Core Principles · Actuarial Statistics · Credibility theory: Bayesian and empirical Bayes credibility premiums
In a Bühlmann model, the expected process variance is 300 and the variance of hypothetical means is 100. How many years of experience n are needed for the credibility factor to reach 0.75?
Nine years are needed. Here k = 300/100 = 3, and solving n/(n+3) = 0.75 gives n = 9. Checking, 9/12 equals 0.75, so nine years of experience give the required credibility factor.
- A6
- B7
- C9Correct
- D12
- 15
Explanation
k = 300/100 = 3. Z = n/(n+3) = 0.75 gives n = 0.75n + 2.25, so 0.25n = 2.25 and n = 9. Check: 9/12 = 0.75. Choosing 6 would give Z = 0.667.
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