## 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.

### MSC:

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

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