Time stochastic s-convexity of claim processes

Denuit, Michel
(2000) Insurance: Mathematics and Economics — Vol. 26, n° 2-3, p. 203-211 (2000)

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Abstract
The purpose of this paper is to study the conditions on a stochastic process under which the s-convex ordering and the s-increasing convex stochastic ordering between two random instants is transformed into a stochastic ordering of the same type between the states occupied by this process at these moments. In this respect, the present work develops a previous study by Shaked and Wong (1995) [Probability in the Engineering and Informational Sciences 9, 563–580]. As an illustration, we show that the binomial and the Poisson processes, commonly used in actuarial sciences to model the occurrence of insured claims, possess this remarkable property.
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Denuit, M. (2000). Time stochastic s-convexity of claim processes. Insurance: Mathematics and Economics, 26(2-3), 203-211. https://doi.org/10.1016/S0167-6687(99)00049-9 (Original work published 2000)