Motivated by [1] and [2], we study in this
paper the optimal (from the insurer's point of view) reinsurance problem when
risk is measured by a general risk measure, namely the GlueVaR distortion risk
measures which is firstly proposed by [3].Suppose an insurer is exposed
to the risk  and decides to buy a reinsurance contract written on the total
claim amounts basis, i.e. the reinsurer covers  and the cedent covers
. In addition, the insurer is obligated to compensate the reinsurer
for undertaking the risk by paying the reinsurance premium, 
( is the safety loading), under the expectation premium principle. Based
on a technique used in [2], this paper derives the optimal ceded loss
functions in a class of increasing convex ceded loss functions. It turns out
that the optimal ceded loss function is of stop-loss type.