Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in problems in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of Range-Value-at-Risk, which includes Value-at-Risk and Expected Shortfall as special cases, we establish new analytical bounds  which we call convolution bounds. These bounds are easy to compute, and we show that they are sharp in many relevant cases. We pay a special attention to the problem of quantile aggregation, and the convolution bounds help us to identify approximations for the extremal dependence structure. The convolution bound enjoys several advantages, including interpretability  , tractability and theoretical properties. 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 .
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based risk measures, we establish new analytical bounds for quantile aggregation which we call convolution bounds. In fact, convolution bounds unify every analytical result and contribute more to the theory of quantile aggregation, and thus these bounds are genuinely the best one available. Moreover, convolution bounds are easy to compute, and we show that they are sharp in many relevant cases. Convolution bounds enjoy several other advantages, including interpretability on the extremal dependence structure, tractability , and theoretical properties. The results directly lead to bounds on the distribution of the sum of random variables with arbitrary dependence, and we illustrate a few applications in operations research .
D
problems in
R
Range-Value-at-Risk, which includes Value-at-Risk and Expected Shortfall as special cases,
quantile-based risk measures,
A
for quantile aggregation
R
These bounds are
In fact, convolution bounds unify every analytical result and contribute more to the theory of quantile aggregation, and thus these bounds are genuinely the best one available. Moreover, convolution bounds are
R
We pay a special attention to the problem of quantile aggregation, and the convolution bounds help us to identify approximations for the extremal dependence structure. The convolution bound enjoys several
Convolution bounds enjoy several other
A
on the extremal dependence structure, tractability
D
tractability
R
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
The results directly lead to
R
. Some applications to operations researchare discussed
with arbitrary dependence, and we illustrate a few applications in operations research