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

A policyholder's claim amount X in a year has conditional mean μ(θ) and variance σ²(θ). Across risks, E[σ²(θ)] = 400 and Var[μ(θ)] = 100. The collective mean is 50. Under Bühlmann credibility, an insured has 4 years of experience with sample mean 70. What is the credibility premium?

The credibility premium is 60. Here k = 400/100 = 4, so Z = 4/(4+4) = 0.5. The premium is 0.5 × 70 + 0.5 × 50 = 60. Answer 66 would wrongly use Z = 0.8.

  1. A60Correct
  2. B62
  3. C64
  4. D66
  5. 70

Explanation

k = E[σ²]/Var[μ] = 400/100 = 4. Z = n/(n+k) = 4/8 = 0.5. Premium = 0.5×70 + 0.5×50 = 60. Using Z=0.8 would give 66.

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