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.

中文翻译：

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对冲价格的可靠估计

我们考虑在交易资产为d $$的无摩擦市场中使用历史股票收益对对冲价格进行统计估计。我们介绍了一种基于经验测度的插件估算器，它显示出一致性，但缺乏合适的鲁棒性。为了解决这个问题，我们提出了新颖的估计器，它使用了较大的larger度量，这是通过围绕经验度量的Wasserstein球的半径与mar密度的允许范数之间的折衷来定义的。然后，我们将研究部分扩展到风险度量的估计，具有交易期权的市场，多周期设置和模型不确定性设置。我们还研究了估计量的收敛速度和超级对冲策略的收敛。