Curricular Concepts in Risk and Insurance.

This article deals with a study which restated the concept of insurer's risk using elementary statistical theorems. In its simplest form the insurer's risk model assumes that the company insures n identical exposure units. In the model the losses of the i-th exposure limit can be represented by the random variable x₁ which can range in value from 0 to V where V is the total amount of insurance written on that exposure unit. The assertion that insurance is possible when the average covariances are equal to zero is supported by a law of large numbers. However, since there is no readily applicable central limit theorem, confidence limits cannot be established. Furthermore, negative correlation is unlikely to be very strong in any insurance situation and will almost certainly not offset a clear catastrophe hazard. Thus, although technically one could quarrel with the statement that independence is necessary for insurance, in fact that assertion is generally true both theoretically and practically. This article has utilized some elementary statistical theorems to restate the concept of insurer's risk and to elaborate upon and extend that concept in such a way as to expose some prevalent fallacies in that topic. It is hoped that this information will be useful to teachers of insurance in presenting material on insurer's risk.