Extremal generators and extremal distributions for the continuous s-convexstochastic orderings

In the first part of this paper, the extremal generators of the continuous s-convex stochastic orderings introduced by Denuit et al., [Denuit, M., Lef evre, Cl., Shaked, M., 1998. Mathematical Inequalities and Applications, 1, 585-613] are identified. Then, the problem of constructing the extremal di stributions with respect to these orderings in moment spaces is reexamined in whole generality using some results given in [De Vylder, EE., 1996. Adva nced Risk Theory. A Self-Contained Introduction. Editions de l'Universite L ibre de Bruxelles, Swiss Association of Actuaries, Bruxelles]. An illustrat ion in life insurance enhances the interest of the theory. (C) 1999 Elsevie r Science B.V. All rights reserved.