Upper and lower bounds for sums of random variables

Authors
Kaas, R Dhaene, J Goovaerts, MJ
Citation
R. Kaas et al., Upper and lower bounds for sums of random variables, INSUR MATH, 27(2), 2000, pp. 151-168
Citations number
17
Categorie Soggetti
Economics
Journal title
INSURANCE MATHEMATICS & ECONOMICS
ISSN journal
01676687 → ACNP
Volume
27
Issue
2
Year of publication
2000
Pages
151 - 168
Database
ISI
SICI code
0167-6687(20001020)27:2<151:UALBFS>2.0.ZU;2-Q
Abstract
In this contribution, the upper bounds for sums of dependent random variabl es X-1 + X-2 + ... + X-n derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution f unctions of the X-i, given Z = z, are known. By a similar technique, lower bounds are derived. A numerical application for the case of lognormal rando m variables is given. (C) 2000 Elsevier Science B.V. All rights reserved.