Measurement of relative inequity and Yaari’s dual theory of risk

We apply Yaari’s dual theory of risk, a type of non-expected utility theory, to the problem of measuring the inequity of a premium relative to the (unknown) net premium. This work parallels that of Promislow and Young [Scandinavian Actuarial Journal, 2000, 121–146]. In the latter work, however, we apply expected utility to the problem of measuring relative inequity. This paper generalizes Yaari’s risk measure, itself a generalization of a well-known measure of inequity called the Gini coefficient.