Before revision:  To the best of our knowledge, there is no other theoretical result on quantile aggregation which is not covered by the convolution bounds, and thus the convolution bounds are genuinely the best one available. The results can be applied to compute bounds on the distribution of the sum of random variables . Some applications to operations researchare discussed .
After revision:  The results directly lead to bounds on the distribution of the sum of random variables . Some applications to operations researchare discussed .