MAS-II: Bühlmann credibility distinguishes noise from heterogeneity

Credibility is not simply the share of data coming from a policyholder. Under the Bühlmann model, the balance depends on process variance, between-risk variance and the number of observations. Specify which parameter represents each source of variation.

Worked example or practice scenario

For n=5, EPV=120 and VHM=30, K=4 and Z=5/9. If observed mean is 140 and collective mean is 100, the credibility estimate is 122.22. More process noise reduces credibility when other quantities are fixed.

Try this next

Double EPV and recompute the weight. Explain why the estimate moves toward the collective mean. Compare this with increasing VHM: greater real differences between risks make the risk’s own observations more valuable.

Reading sources

• Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.