De minimis and equity in risk

Indices and orderings are developed for evaluating alternative strategies in the management of risk. They reflect the goals of reducing individual and collective risks, of increasing equity, and of assigning priority to the reduction and to the equity of high risks. Individual risk is defined as the (random or non-random) level of exposure to a danger. In particular the role of a lower negligibility level is investigated. A class of indices is proposed which involves two parameters, a negligibility level and a parameter of inequality aversion, and several interpretations of the indices are discussed. We provide a set of eight axioms which are necessary and sufficient for this class of indices, and we present an approach to deal with partial information on the parameters.