Before revision:  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.
After revision:  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 for quantile aggregation which we call convolution bounds.