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

In the Bühlmann model, which change would increase the credibility factor Z for a given policyholder, other things equal?

A larger variance of the hypothetical means increases Z. It reduces k = E[s²]/Var[m], so the policyholder's own experience gets more weight because risks genuinely differ. The collective mean does not affect Z.

  1. AA larger expected process variance E[s²(θ)]
  2. BA smaller variance of the hypothetical means Var[m(θ)]
  3. CFewer years of observed experience n
  4. DA larger variance of the hypothetical means Var[m(θ)]Correct
  5. A change in the collective mean only

Explanation

Z = n/(n+k) with k = E[s²]/Var[m]. Raising Var[m] lowers k and so raises Z. Raising E[s²] or lowering n reduces Z, and the collective mean does not enter Z.

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