Skip to content

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

In empirical Bayes credibility Model 1 with a fixed number of years n per risk, which statement about the credibility factor Z = n/(n+k), with k = E[s²(θ)]/Var[m(θ)], is correct?

Z rises with more years and with greater differences between risks (higher variance of hypothetical means), and falls when the expected process variance is higher. This follows from Z = n/(n+k), where k is process variance divided by variance of hypothetical means.

  1. AZ decreases as the variance of the hypothetical means increases.
  2. BZ increases as the expected process variance increases.
  3. CZ increases with n and with the variance of the hypothetical means, and decreases as the expected process variance increases.Correct
  4. DZ does not depend on the number of years n.
  5. Z equals 1 whenever a risk's sample mean differs from the overall mean.

Explanation

A larger Var[m] lowers k and raises Z, as the risks differ more and own experience is more informative. A larger process variance raises k and lowers Z, because experience is noisier. More years n also raises Z. Z does not depend on the sample mean values themselves.

Did you get it right without looking?

One question tells you little. A timed set on Credibility theory: Bayesian and empirical Bayes credibility premiums shows your real accuracy, how long you take and where you lose marks.

Practise Credibility theory: Bayesian and empirical Bayes credibility premiumsFree diagnostic mock

More Credibility theory: Bayesian and empirical Bayes credibility premiums questions