Extremal generators and extremal distributions for the continuous s-convex stochastic 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., Lefèvre, Cl., Shaked, M., 1998. Mathematical Inequalities and Applications, 1, 585–613] are identified. Then, the problem of constructing the extremal distributions with respect to these orderings in moment spaces is reexamined in whole generality using some results given in [De Vylder, F.E., 1996. Advanced Risk Theory. A Self-Contained Introduction. Editions de l’Université Libre de Bruxelles, Swiss Association of Actuaries, Bruxelles]. An illustration in life insurance enhances the interest of the theory.