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

Which statement about the Bayesian credibility premium under squared error loss is correct?

The Bayesian premium under squared error loss is the posterior mean of the expected claim, E[X | data]. The median corresponds to absolute error loss and the prior mode is unrelated to the observed data.

  1. AIt is the posterior median of the risk parameter
  2. BIt is the mode of the prior distribution
  3. CIt is the posterior mean of the claim distribution's mean, E[X | data]Correct
  4. DIt always equals the sample mean when the prior is informative
  5. It is independent of the number of years of data observed

Explanation

Squared error loss is minimised by the posterior mean, so the premium is E[E(X|θ) | data]. The median minimises absolute error loss, not squared error. The premium moves towards the sample mean as data grows, but does not equal it with an informative prior.

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