Upper and Lower Bounds for Sums of Random Variables.

18 Pages Posted: 21 Feb 2006

See all articles by Rob Kaas

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

Jan Dhaene

Katholieke Universiteit Leuven

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Abstract

In this contribution, the upper bounds for sums of dependent random variables X1 + X2 +...+ Xn derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution functions of the Xi, 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.

Keywords: Dependent risks, Comonotonicity, Convex order, Cash-flows, Present values, Stochastic annuities

Suggested Citation

Kaas, Rob and Dhaene, Jan and Goovaerts, Marc, Upper and Lower Bounds for Sums of Random Variables.. Insurance: Mathematics & Economics, Vol, 27, No. 2, pp. 151-168, 2000, Available at SSRN: https://ssrn.com/abstract=884108

Rob Kaas (Contact Author)

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Jan Dhaene

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

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