Upper and lower bounds for sums of random variables. (English) Zbl 0989.60019

In actuarial sciences, the stop-loss order and convex order concepts are closely related, hence it seems naturally to study upper and lower bounds for sums \(X_1 + X_2 + \ldots + X_n\) of dependent random variables in the sense of convex order. The paper gives such an answer, under mild hypothesis: the marginal distribution of each \(X_i\) is known, and there exists a random variable \(Z\) such that the distribution functions of \(X_i\), given \(Z=z\), are known. A numerical illustration is given in the case of lognormal random variables.


60E15 Inequalities; stochastic orderings
91B28 Finance etc. (MSC2000)
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