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

In a Poisson–Gamma model the prior mean claim frequency is 0.2 per year and the prior Gamma shape is 2 (rate 10). A policyholder has 0 claims in 10 years. What is the Bayesian credibility premium?

The posterior is Gamma(2, 20), giving a premium of 2/20 = 0.1 claims per year. A claim-free decade lowers the estimate from the prior 0.2 but not to zero, because the prior still carries weight.

  1. A0.200
  2. B0.100Correct
  3. C0.000
  4. D0.150
  5. 0.050

Explanation

Posterior is Gamma(2 + 0, 10 + 10) = Gamma(2, 20). Mean = 2/20 = 0.1. Option 0.000 ignores the prior, while 0.2 ignores the data.

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