Credibility models were first proposed in the beginning of the twentieth century to update predictions of insurance losses in light of recently available data of insurance claims. The oldest approach is the limited-fluctuation credibility method, also called the classical approach, which proposes to update the loss prediction as a weighted average of the prediction based purely on the recent data and the rate in the insurance manual. Full credibility is achieved if the amount of recent data is sufficient, in which case the updated prediction will be based on the recent data only. If, however, the amount of recent data is insufficient, only partial credibility is attributed to the data and the updated prediction depends on the manual rate as well.

We consider the calculation of the minimum size of the data above which full credibility is attributed to the data. For cases where the data are insufficient we derive the partial-credibility factor and the updating formula for the prediction of the loss. The classical credibility approach is applied to update the prediction of loss measures such as the frequency of claims, the severity of claims, the aggregate loss, and the pure premium of a block of insurance policies.

Learning objectives

1. Basic framework of credibility

2. The limited-fluctuation (classical) credibility approach

3. Full credibility

4. Partial credibility

5. Prediction of claim frequency, claim severity, aggregate loss, and pure premium