Risk Theory pp 47-70 | Cite as

# Credibility Theory

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## Abstract

A collective contract is determined by the distribution of the annual aggregate claim. For a fair premium one therefore needs to calculate the expected value of the annual claim. But its distribution is unknown. A way to circumvent the lack of knowledge are Bayesian methods. As joint distributions are hard to obtain, one uses a linear prediction of the aggregate claims. These credibility methods are known under the name “Bühlmann model” or “Bühlmann-Straub model”. We further consider Bonus-Malus systems as a simple approximation to the credibility premium.

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© Springer International Publishing AG, part of Springer Nature 2017