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On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang‐Bang No‐Arbitrage Criteria

Author

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  • Igor V. Evstigneev
  • Klaus Schürger
  • Michael I. Taksar

Abstract

The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton, and Willinger (1990) in the following two respects: (a) the result is extended to a model with general portfolio constraints, and (b) versions of the no‐arbitrage criterion based on the bang‐bang principle in control theory are developed.

Suggested Citation

  • Igor V. Evstigneev & Klaus Schürger & Michael I. Taksar, 2004. "On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang‐Bang No‐Arbitrage Criteria," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 201-221, April.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:2:p:201-221
    DOI: 10.1111/j.0960-1627.2004.00189.x
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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. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    3. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    4. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    5. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    6. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    7. 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.
    8. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    9. 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.
    10. 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.
    11. Chen, Shumin & Liu, Yanchu & Weng, Chengguo, 2019. "Dynamic risk-sharing game and reinsurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 216-231.

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