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February 2021 Robust estimation of superhedging prices
Jan Obłój, Johannes Wiesel
Ann. Statist. 49(1): 508-530 (February 2021). DOI: 10.1214/20-AOS1966

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.

Citation

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Jan Obłój. Johannes Wiesel. "Robust estimation of superhedging prices." Ann. Statist. 49 (1) 508 - 530, February 2021. https://doi.org/10.1214/20-AOS1966

Information

Received: 1 August 2019; Revised: 1 March 2020; Published: February 2021
First available in Project Euclid: 29 January 2021

Digital Object Identifier: 10.1214/20-AOS1966

Subjects:
Primary: 62G20, 62G35, 91G20, 91G70

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • February 2021
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