24.1 Introductory material
24.1.1 The nature of credibility theory
Suppose that X is the random variable denoting claims on an insurance policy during a specific period, and an insurer charges E(X) as a net premium for each individual. Of course, a typical group of purchasers is not homogenous and there will be both bad and good risks within the group, but these cannot normally be identified as such at the outset of the contract. This means that some are paying more than they should be and some less. Suppose, however, that after issuance of the policy, the insurer is presented with additional information on a policyholder, usually as the result of claim experience, which provides some indication as to the degree of risk. For example, a purchaser of automobile insurance incurs a few costly claims. Does this indicate they are a poor driver, and their subsequent premiums should increase, or could they really be good drivers with the costly claims simply a result of bad luck? Credibility theory deals with the problem of analyzing this additional information and deciding on how it should be used to modify future premiums. The key question then is, how ‘credible’ is the additional data, providing the source for the name of this concept.
24.1.2 Information assessment
We first explore the basic idea of utilizing information to reassess probabilities, beginning with a few simple examples.
Example 24.1 A bag contains three dies. Two of these are standard, having ...