credibility premium

After all the variance estimating and Z calculating, what an actuary actually hands over is a number: next period's premium (or expected loss) for this particular risk. The credibility premium is that number — the credibility-weighted blend of the risk's own experience and the collective mean, used to price or reserve for the coming period. It is the practical output of credibility theory, the thing that goes on the renewal notice.

It is just the credibility formula applied to a premium: credibility premium = Z times (the risk's own observed average) plus (1 minus Z) times (the overall mean of the collective). Under Buhlmann this is the best linear estimate of the risk's true future cost. A worked case: a group's own average claim is 1,150 per member, the manual (collective) rate is 1,000, and the Buhlmann Z works out to 0.7, so the credibility premium is 0.7 times 1,150 plus 0.3 times 1,000 = 1,105 per member. Next year, with another year of data, Z and the premium update again.

Credibility premiums are the engine of experience rating: the bigger and more distinctive a risk's record, the more its own premium reflects its own losses, which rewards good risks and prices bad ones fairly. Two honest points: the credibility premium estimates expected cost, so it must still be loaded for expenses, profit and risk margins to become a sellable gross premium; and it is only as fair as the collective it blends toward — if the 'manual rate' lumps together risks that should be separated, even a perfect Z passes that unfairness through.