On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints
dc.contributor.author | Bayraktar, Erhan | |
dc.contributor.author | Zhou, Zhou | |
dc.date.accessioned | 2017-10-05T18:17:58Z | |
dc.date.available | 2019-01-07T18:34:36Z | en |
dc.date.issued | 2017-10 | |
dc.identifier.citation | Bayraktar, Erhan; Zhou, Zhou (2017). "On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints." Mathematical Finance 27(4): 988-1012. | |
dc.identifier.issn | 0960-1627 | |
dc.identifier.issn | 1467-9965 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/138293 | |
dc.description.abstract | We 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.publisher | Springer | |
dc.publisher | Wiley Periodicals, Inc. | |
dc.subject.other | fundamental theorem of asset pricing | |
dc.subject.other | optional decomposition | |
dc.subject.other | portfolio constraints | |
dc.subject.other | model uncertainty | |
dc.subject.other | sub‐(super‐)hedging | |
dc.title | On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints | |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbsecondlevel | Finance | |
dc.subject.hlbtoplevel | Business and Economics | |
dc.subject.hlbtoplevel | Science | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/138293/1/mafi12104_am.pdf | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/138293/2/mafi12104.pdf | |
dc.identifier.doi | 10.1111/mafi.12104 | |
dc.identifier.source | Mathematical Finance | |
dc.identifier.citedreference | Bayraktar, E., Y.‐J. Huang, and Z. Zhou ( 2015 ): On Hedging American Options under Model Uncertainty, SIAM J. Financ. Math. 6 ( 1 ), 425 – 447. | |
dc.identifier.citedreference | Aliprantis, C. D., and K. C. Border ( 2006 ): Infinite Dimensional Analysis. A Hitchhiker’s Guide, 3rd ed., Berlin: Springer. | |
dc.identifier.citedreference | Acciaio, 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. | |
dc.identifier.citedreference | Nutz, M. ( 2016 ): Utility Maximization under Model Uncertainty in Discrete Time, Math. Finance 26 ( 2 ), 252 – 268. | |
dc.identifier.citedreference | Föllmer, 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.citedreference | Czichowsky, 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.citedreference | Cohn, D. L. ( 2013 ): Measure Theory, 2nd ed., Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], New York: Birkhäuser/Springer. | |
dc.identifier.citedreference | Bouchard, B., and M. Nutz, ( 2015 ): Arbitrage and Duality in Nondominated Discrete‐Time Models, Ann. Appl. Probab. 25 ( 2 ), 823 – 859. | |
dc.identifier.citedreference | Bertsekas, 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.owningcollname | Interdisciplinary and Peer-Reviewed |
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