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On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints
dc.contributor.authorBayraktar, Erhan
dc.contributor.authorZhou, Zhou
dc.date.accessioned2017-10-05T18:17:58Z
dc.date.available2019-01-07T18:34:36Zen
dc.date.issued2017-10
dc.identifier.citationBayraktar, Erhan; Zhou, Zhou (2017). "On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints." Mathematical Finance 27(4): 988-1012.
dc.identifier.issn0960-1627
dc.identifier.issn1467-9965
dc.identifier.urihttps://hdl.handle.net/2027.42/138293
dc.description.abstractWe consider the fundamental theorem of asset pricing (FTAP) and the hedging prices of options under nondominated model uncertainty and portfolio constraints in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super‐martingale under these measures. We also get the nondominated optional decomposition with constraints. From this decomposition, we obtain the duality of the super‐hedging prices of European options, as well as the sub‐ and super‐hedging prices of American options. Finally, we get the FTAP and the duality of super‐hedging prices in a market where stocks are traded dynamically and options are traded statically.
dc.publisherSpringer
dc.publisherWiley Periodicals, Inc.
dc.subject.otherfundamental theorem of asset pricing
dc.subject.otheroptional decomposition
dc.subject.otherportfolio constraints
dc.subject.othermodel uncertainty
dc.subject.othersub‐(super‐)hedging
dc.titleOn Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints
dc.typeArticleen_US
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbsecondlevelFinance
dc.subject.hlbtoplevelBusiness and Economics
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/138293/1/mafi12104_am.pdf
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/138293/2/mafi12104.pdf
dc.identifier.doi10.1111/mafi.12104
dc.identifier.sourceMathematical Finance
dc.identifier.citedreferenceBayraktar, E., Y.‐J. Huang, and Z. Zhou ( 2015 ): On Hedging American Options under Model Uncertainty, SIAM J. Financ. Math. 6 ( 1 ), 425 – 447.
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dc.identifier.citedreferenceAcciaio, B., M. Beiglböck, F. Penkner, and W. Schachermayer ( 2016 ): A Model‐Free Version of the Fundamental Theorem of Asset Pricing and the Super‐Replication Theorem, Math. Finance 26 ( 2 ), 233 – 251.
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dc.identifier.citedreferenceFöllmer, H., and A. Schied ( 2004 ): Stochastic Finance: An Introduction in Discrete Time, vol. 27 of de Gruyter Studies in Mathematics, extended ed., Berlin: Walter de Gruyter & Co.
dc.identifier.citedreferenceCzichowsky, C., and M. Schweizer: Closedness in the Semimartingale Topology for Spaces of Stochastic Integrals with Constrained Integrands, in Séminaire de Probabilités XLIII, vol. 2006 of Lecture Notes in Math., Berlin: Springer, 2011, pp. 413 – 436.
dc.identifier.citedreferenceCohn, D. L. ( 2013 ): Measure Theory, 2nd ed., Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], New York: Birkhäuser/Springer.
dc.identifier.citedreferenceBouchard, B., and M. Nutz, ( 2015 ): Arbitrage and Duality in Nondominated Discrete‐Time Models, Ann. Appl. Probab. 25 ( 2 ), 823 – 859.
dc.identifier.citedreferenceBertsekas, D. P., and S. E. Shreve ( 1978 ): Stochastic Optimal Control: The Discrete‐Time Case, vol. 139 of Mathematics in Science and Engineering, New York: Academic Press Inc.
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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