ROBUST ESTIMATION OF SUPERHEDGING PRICES

• 成果类型: Article
• 署名作者: Obloj, Jan; Wiesel, Johannes
• 署名单位: University of Oxford; University of Oxford
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1966
• 发表日期: 2021
• 页码: 508-530
• 关键词: Risk measures; nonparametric-estimation; Wasserstein Distance; CONVERGENCE; BOUNDARY; support

摘要

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.