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IAI Actuarial Core Principles · Actuarial Statistics · Credibility theory: Bayesian and empirical Bayes credibility premiums

Given θ, claim amounts X are Normal(θ, variance 400). The prior for θ is Normal(mean 1000, variance 100). One observation x = 1100 is made. What is the Bayesian credibility premium for the next claim amount?

The credibility factor is 1/(1 + 400/100) = 0.2, so the premium is 0.2×1100 + 0.8×1000 = 1020 rupees. The prior is much tighter than the claim variance, so the premium stays close to the prior mean.

  1. A1020Correct
  2. B1050
  3. C1080
  4. D1100
  5. 1000

Explanation

Z = n/(n + σ²/τ²) = 1/(1 + 400/100) = 0.2. Premium = 0.2×1100 + 0.8×1000 = 1020. Option 1050 would be wrong because it gives equal weight to prior and data.

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