Upper and lower bounds for sums of random variables

Upper and lower bounds for sums of random variables

In this contribution, the upper bounds for sums of dependent random variables 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 functions of the X i , given Z= z, are known. By a similar technique, lower bounds...

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Veröffentlicht in:Insurance, mathematics & economics mathematics & economics, 2000-10, Vol.27 (2), p.151-168
Hauptverfasser: Kaas, Rob, Dhaene, Jan, Goovaerts, Marc J.
Format: Artikel
Sprache:eng
Schlagworte:
Cash-flows
Comonotonicity
Convex order
Dependent risks
Distribution
Mathematical economics
Mathematical methods
Mathematical models
Payments
Present values
Stochastic annuities
Stochastic processes
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Zusammenfassung:In this contribution, the upper bounds for sums of dependent random variables 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 functions 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 random variables is given.
ISSN:0167-6687
1873-5959
DOI:10.1016/S0167-6687(00)00060-3