par Denuit, Michel 
;Genest, Christian;Marceau, Étienne Tienne E.
Référence Insurance. Mathematics & economics, 25, 1, page (85-104)
Publication Publié, 1999-09
;Genest, Christian;Marceau, Étienne Tienne E.Référence Insurance. Mathematics & economics, 25, 1, page (85-104)
Publication Publié, 1999-09
Article révisé par les pairs
| Résumé : | There is a growing concern in the actuarial literature for the effect of dependence between individual risks Xi on the distribution of the aggregate claim S=X1++Xn. Recent work by Dhaene and Goovaerts (Dhaene, J., Goovaerts, M.J., 1996. ASTIN Bulletin 26, 201-212; Dhaene, J., Goovaerts, M.J., 1997. Insurance: Mathematics and Economics 19, 243-253) and Müller (Müller, A., 1997a. Insurance: Mathematics and Economics 21, 219-223; Müller, A., 1997b. Advances in Applied Probability 29, 414-428) has led, among other things, to the identification of the portfolio yielding the smallest and largest stop-loss premiums and hence to bounds on E{φ(S)} for arbitrary non-decreasing, convex functions φ in situations of dependence between the Xi's. This paper extends these results by showing how to compute bounds on P(S>s) and more generally on E{φ(S)} for monotone, but not necessarily convex functions φ. Special attention is paid to the numerical implementation of the results and examples of application are provided. © 1999 Elsevier Science B.V. |
