With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor minimizes the cost of hedging a path dependent contingent claim with a given expected success ratio, in a discrete-time, semi-static market of stocks and options. We prove duality results that link the problem of quantile hedging to a randomized composite hypothesis test . Then by assuming a compact path space , an arbitrage-free discretization of the market is proposed as an approximation. 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. Finally, the performance of the approximate hedging strategy in the original market  and the convergence of the  quantile hedging price are analyzed.
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor 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 enables numerical calculation of the quantile hedging price by applying the generalized Neyman-Pearson Lemma. Finally, the performance in the original market of the approximating hedging strategy and the convergence of the approximating quantile hedging price are analyzed.
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