Time stochastic s-convexity of claim processes

The purpose of this paper is to study the conditions on a stochastic proces s under which the s-convex ordering and the s-increasing convex stochastic ordering between two random instants is transformed into a stochastic order ing of the same type between the states occupied by this process at these m oments. In this respect, the present work develops a previous study by Shak ed and Wong (1995) [Probability in the Engineering and Informational Scienc es 9, 563-580]. As an illustration, we show that the binomial and the Poiss on processes, commonly used in actuarial sciences to model the occurrence o f insured claims, possess this remarkable property. (C) 2000 Elsevier Scien ce B.V. All rights reserved.