Before revision:  We also study convergence rates, convergence of superhedging strategies, and our study extends , in part, to the case of a market with traded options and to a multiperiod setting  .
After revision:  We establish consistency and robustness of these estimators and argue that they offer a superior performance relative to the plugin estimator. We generalise the results by replacing the superhedging criterion with acceptance relative to a risk measure. We further extend our study , in part, to the case of a market with traded options and to a multiperiod setting .