On s-convex stochastic extrema for arithmetic risks

Recently, Denuit and Lefevre (Insurance: Mathematics and Economics 20 (1997 ) 197-213) have introduced a class of discrete s-convex stochastic ordering s for comparing arithmetic risks in actuarial sciences inter alia. The pres ent paper is concerned with the construction of the extremal distributions with respect to these orderings. Firstly, the general Problem of bounding s uch risks is studied in some details. Then, improved extrema are obtained f or the case where the risks are known to have a decreasing density function . For illustration, the results are applied to derive bounds for the probab ility of ruin in the compound binomial risk model. (C)1999 Elsevier Science B.V. All rights reserved.