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

In Bühlmann credibility, which change would increase the credibility factor Z for a given risk?

Increasing the number of years of observation raises Z. Since Z = n/(n + k) with k = E[σ²]/Var[μ], larger n increases credibility, whereas higher process variance or lower variance of hypothetical means increases k and reduces Z. The means themselves do not affect Z.

  1. AIncreasing the expected process variance E[σ²(θ)]
  2. BDecreasing the variance of the hypothetical means Var[μ(θ)]
  3. CIncreasing the number of years of observation nCorrect
  4. DMoving the collective mean closer to the sample mean
  5. Reducing the sample mean of the risk

Explanation

Z = n/(n + E[σ²]/Var[μ]). Raising n raises Z. A higher process variance or a lower variance of hypothetical means raises k and lowers Z. The sample and collective means do not enter Z.

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