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

The full credibility standard for claim frequency is 1,082 claims. Claim severity has coefficient of variation 2. Using the standard limited fluctuation approach for the number of claims needed to give full credibility to aggregate (pure premium) losses with Poisson frequency, which number of claims is required?

The standard is 5,410 claims. For aggregate losses with Poisson frequency, the frequency standard is multiplied by one plus the squared coefficient of variation of severity: 1,082 × (1 + 2²) = 5,410. Multiplying by CV² alone would give 4,328, which is wrong.

  1. A1,082
  2. B2,164
  3. C4,328
  4. D5,410Correct
  5. 3,246

Explanation

Pure premium standard = n_freq × (1 + CV²) = 1082 × (1 + 4) = 5,410. 4,328 is wrong because it multiplies by CV² = 4 and omits the 1.

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