Upper and Lower Bounds for Sums of Random Variables.
18 Pages Posted: 21 Feb 2006
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
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