Robust estimation of superhedging prices

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with $d$ traded assets. introduce plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use larger set martingale defined through tradeoff between the radius Wasserstein balls around measure allowed norm densities. then extend our study, part, to risk measures, case markets options, multi-period setting settings model uncertainty. also study convergence rates super-hedging strategies.