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A characterization of the dilation order and its applications |
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| Authors: | Enrico Fagiuoli Franco Pellerey Moshe Shaked |
| Institution: | (1) Dipartiment di Matematica, Università di Milano, Via L. Cicognara, 7, I-20129 Milano, Italy;(2) Dipartimento di Matematica Statistica, Informatica e Applicazioni, Università degli Studi di Bergamo, Piazza Rosate, 2, I-24129 Bergamo, Italy;(3) Department of Mathematics, University of Arizona, 85721 Tucson, AZ, USA |
| Abstract: | LetX andY be two random variables with finite expectationsE X andE Y, respectively. ThenX is said to be smaller thanY in the dilation order ifEϕ(X-E X)]≤Eϕ(Y-E Y)] for any convex functionϕ for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization enables us to give new interpretations to the dilation order, and using them we identify conditions which imply the dilation order. A sample of applications of the new characterization is given. Partially supported by MURST 40% Program on Non-Linear Systems and Applications. Partially supported by “Gruppo Nazionale per l'Analisi Funzionale e sue Applicazioni”—CNR. |
| Keywords: | Excess wealth order dilation order convex order location independent risks comparison comparison of variances |
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