IAI Actuarial Core Principles · Actuarial Statistics · Credibility theory: Bayesian and empirical Bayes credibility premiums
Given θ, annual claim amounts X are Normal(θ, 400) (variance 400). The prior for θ is Normal(mean 1000, variance 100). One year's claim of 1,200 is observed. What is the Bayesian premium for next year?
The premium is 1,040. Normal-Normal credibility gives Z = prior variance divided by (prior variance + claim variance) = 100/500 = 0.2, so the premium is 0.2 × 1,200 + 0.8 × 1,000 = 1,040.
- A1,040Correct
- B1,100
- C1,160
- D1,000
- 1,200
Explanation
With n = 1, Z = 100/(100 + 400) = 0.2. Premium = 0.2×1200 + 0.8×1000 = 240 + 800 = 1,040. The answer 1,160 results from using Z = 0.8, which swaps the weights.
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