Partial Credibility

Study guide: Exam MAS-II

Partial credibility is the weight Z < 1 that classical credibility gives to experience that falls short of the Full Credibility Standard. The square-root rule sets Z so that the credibility-weighted estimate has the same variance the full-credibility standard was chosen to deliver.

Z = \min\left(\sqrt{\frac{n}{n_F}},\; 1\right)

• n is the observed volume and n_F the Full Credibility Standard, both in the same units (claims, or exposures)
• The square root, not the ratio: the standard deviation of the mean falls with \sqrt{n}, so halving the variance gap takes four times the data
• Z multiplies the observed experience; 1 - Z goes to the Complement of Credibility
• Partial credibility stabilizes the estimate but is biased toward the complement — it makes no claim to minimize squared error, which is what Bühlmann Credibility is for
• Z is capped at 1: extra data beyond the standard never earns more than full weight

Credibility-Weighting a Small Class A rating class produced 300 claims against a full-credibility standard of 1,082. Its observed pure premium is 420; the manual (complement) pure premium is 380. Find the credibility-weighted pure premium.

Answer Z = \sqrt{\frac{300}{1{,}082}} = \sqrt{0.2773} = 0.527 \text{PP} = 0.527(420) + 0.473(380) = 221.3 + 179.7 = 401.0 The class gets 401, a little over half of the way from the manual rate to its own experience.