Robust estimation of superhedging prices
The Annals of Statistics · 2021 · Volume 49 · Issue 1
Abstract
We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with $d$ traded assets. We introduce a 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 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 then extend our study, in part, to estimation of risk measures, to the case of markets with traded options, to a multi-period setting and to settings with model uncertainty. We also study convergence rates of estimators and convergence of super-hedging strategies.
Keywords
62G20, 62G35, 91G20, 91G70, consistency, empirical measure, pricing-hedging duality, risk measures, robustness, statistical estimation, stock returns, Superhedging price, Wasserstein metric
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