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No Arbitrage in Discrete Time Under Portfolio Constraints

Author

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  • Laurence Carassus
  • Huye^n Pham
  • Nizar Touzi

Abstract

In frictionless securities markets, the characterization of the no‐arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).

Suggested Citation

  • Laurence Carassus & Huye^n Pham & Nizar Touzi, 2001. "No Arbitrage in Discrete Time Under Portfolio Constraints," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 315-329, July.
    • Handle: RePEc:bla:mathfi:v:11:y:2001:i:3:p:315-329
    DOI: 10.1111/1467-9965.00117
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    Citations

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    Cited by:

    1. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    2. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    3. Xiangyu Cui & Duan Li & Xun Li, 2014. "Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure," Papers 1403.0718, arXiv.org.
    4. Stefan Gerhold & Paul Kruhner, 2017. "Dynamic trading under integer constraints," Papers 1708.07661, arXiv.org.
    5. Philippe ARTZNER & Karl-Theodor EISELE & Thorsten SCHMIDT, 2022. "Insurance-Finance Arbitrage," Working Papers of LaRGE Research Center 2022-09, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    6. X. Chao & K. Lai & Shou-Yang Wang & Mei Yu, 2005. "Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs," Annals of Operations Research, Springer, vol. 135(1), pages 211-221, March.
    7. Evstigneev, Igor V. & Schürger, Klaus & Taksar, Michael I., 2002. "On the fundamental theorem of asset pricing: random constraints and bang-bang no-arbitrage criteria," Bonn Econ Discussion Papers 24/2002, University of Bonn, Bonn Graduate School of Economics (BGSE).
    8. Xun Li & Zuo Quan Xu, 2015. "Continuous-Time Mean-Variance Portfolio Selection with Constraints on Wealth and Portfolio," Papers 1507.06850, arXiv.org.
    9. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    10. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    11. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    12. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    13. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    14. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    15. Stefan Gerhold & Paul Krühner, 2018. "Dynamic trading under integer constraints," Finance and Stochastics, Springer, vol. 22(4), pages 919-957, October.
    16. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    17. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    18. Takuji Arai, 2016. "Good deal bounds with convex constraints: --- examples and proofs ---," Keio-IES Discussion Paper Series 2016-017, Institute for Economics Studies, Keio University.
    19. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    20. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    21. Takuji Arai, 2017. "Good Deal Bounds With Convex Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-15, March.

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