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

In the Bühlmann-Straub model, the variance of the claim ratio X_ij given θ_i is s²(θ_i)/m_ij. What does this assumption imply?

Observed claim ratios have lower variance when exposure is larger, since variance is s²(θ)/m. Years with more exposure are more reliable and receive greater weight in the credibility estimate.

  1. AVariance of observed ratios falls as exposure risesCorrect
  2. BVariance of observed ratios rises with exposure
  3. CVariance is the same for all exposures
  4. DClaim ratios are perfectly correlated across years
  5. Hypothetical means depend on exposure

Explanation

Dividing by m_ij means larger exposure gives a smaller variance, so observations with larger exposure are more reliable and weighted more heavily.

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