Statistical estimation of superhedging prices
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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.
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