We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a simple plugin estimator based on empirical measures , show it is consistent but lacks suitable robustness. This is addressed by our improved estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. 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  .
We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. 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 markets with traded options , to a multiperiod setting and to settings with model uncertainty. We also study convergence rates of estimators and convergence of superhedging strategies .
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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
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and to settings with model uncertainty. We also study convergence rates of estimators and convergence of superhedging strategies