Before revision:  The discretized market has a dominating measure, which enables us to calculate the quantile hedging price and the associated hedging strategy by using the generalized Neyman-Pearson Lemma.
After revision:  The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and enables numerical calculation of the quantile hedging price and the associated hedging strategy by using the generalized Neyman-Pearson Lemma.