An Introduction to Credibility Theory

Robert Kairis

Credibility theory has its roots in early 20th century actuarial science, but has become mainstream mathematics. Its basic aim is to optimise an estimate by combining multiple pieces of information and giving each an appropriate weighting.

In an actuarial context, this could be estimating the mortality rate of a pension scheme by combining the scheme’s specific historical mortality experience with a “prior view” estimate derived from a rating factor model built using the historical mortality experience data from a wider group of similar pension schemes.

An estimate using only the scheme’s historical mortality experience could be quite uncertain, depending on the size of the scheme’s data set, although it may have a low bias. An estimate using a rating factor approach may have a lower sampling error due to the larger volume of data. However, it would be a biased estimate, which brings in its own uncertainty. Credibility theory shows that the optimal approach is to take a weighted average of both an individual scheme’s experience and that of a wider group of other similar schemes, and also helps to address the weight given to each.

In this chapter we provide a brief history

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