Robust estimation of superhedging prices
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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Institute of Mathematical Statistics
2021
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| _version_ | 1826280057069371392 |
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| author | Obloj, J Wiesel, J |
| author_facet | Obloj, J Wiesel, J |
| author_sort | Obloj, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:08:00Z |
| format | Journal article |
| id | oxford-uuid:7836742d-2df3-4996-b2cd-66d408086c4e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:08:00Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:7836742d-2df3-4996-b2cd-66d408086c4e2022-03-26T20:29:17ZRobust estimation of superhedging pricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7836742d-2df3-4996-b2cd-66d408086c4eEnglishSymplectic ElementsInstitute of Mathematical Statistics2021Obloj, JWiesel, JWe 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. |
| spellingShingle | Obloj, J Wiesel, J Robust estimation of superhedging prices |
| title | Robust estimation of superhedging prices |
| title_full | Robust estimation of superhedging prices |
| title_fullStr | Robust estimation of superhedging prices |
| title_full_unstemmed | Robust estimation of superhedging prices |
| title_short | Robust estimation of superhedging prices |
| title_sort | robust estimation of superhedging prices |
| work_keys_str_mv | AT oblojj robustestimationofsuperhedgingprices AT wieselj robustestimationofsuperhedgingprices |