Lorenz and Excess Wealth Orders, with Applications in Reinsurance Theory

The purpose of this paper is to study the stochastic orderings defined by means of pointwise comparison of the Lorenz curves, or of the excess wealth transforms, of two risks. The resulting order relations are presented in an actuarial context and put in relation with classical stochastic orderings, namely the stochastic dominance, the stop-loss order, the convex order and the dispersive order. Several relevant applications in reinsurance theory are provided.