Credibility theory

Credibility theory answers a fundamental practical question of actuarial science, namely how much confidence to place in a risk's own experience relative to a broader reference when pricing. If one has a great deal of data on a risk, its experience is statistically reliable and one can largely rely on it. If one has only a little, that experience is too unstable to be taken at face value, and it is better to weight it against a market reference. Credibility formalizes this trade-off by assigning the risk's own experience a weight, between zero and one, increasing with the volume and stability of the data, the complement being placed on the reference. The final pricing is thus a weighted average between individual experience and the collective average, which avoids both over-reacting to a few isolated losses and ignoring a real specificity. This framework, formalized notably by Bühlmann, is omnipresent in pricing. In cyber insurance, the credibility of a risk's own data is generally low, for lack of a sufficient and stable track record, which leads to giving significant weight to market references and expert judgment, at the cost of a less fine segmentation.

A company has had only a single cyber loss in five years. Rather than pricing on this too-thin basis, the actuary weights this individual experience, of low credibility, against the average loss experience of its sector, which is far more robust.

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