On s-convex extrema for t-monotone distributions, with applications

Claude Lefèvre (1) , Stéphane Loisel (2)

1 ULB - Département de Mathématique [Bruxelles]
2 SAF - Laboratoire de Sciences Actuarielle et Financière

Our purpose in this paper is to provide a new and unifying approach to construct s-convex stochastic extrema for distributions that are known to be t-monotone. A key point is that such a monotonicity property on the distributions can be removed by having recourse to the stationary-excess operator and its iterates. Both discrete and continuous cases are investigated. Several extremal distributions under monotonicity conditions are obtained in explicit form. Their use is illustrated with some applications to insurance.

Mots clés: Discrete and continuous versions; Insurance risks; s-convex stochastic orders; Extremal distributions; t-monotone distributions; Stationary-excess operator; Discrete and continuous versions.

Domaines: Economies et finances; Probabilités [math.PR]

Claude Lefèvre, Stéphane Loisel. On s-convex extrema for t-monotone distributions, with applications. 2009. ⟨hal-00442047v1⟩