Quantile Hedging in a Semi-Static Market with Model Uncertainty

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.