  With model uncertainty characterized by a convex, possibly non-dominated set
of probability measures, the agent minimizes the cost of hedging a path
dependent contingent claim with given expected success ratio, in a
discrete-time, semi-static market of stocks and options. Based on duality
results which link quantile hedging to a randomized composite hypothesis test,
an arbitrage-free discretization of the market is proposed as an approximation.
The discretized market has a dominating measure, which guarantees the existence
of the optimal hedging strategy and helps numerical calculation of the quantile
hedging price. As the discretization becomes finer, the approximate quantile
hedging price converges and the hedging strategy is asymptotically optimal in
the original market.
