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On the fundamental theorem of asset pricing: random constraints and bang-bang no-arbitrage criteria

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

Abstract

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

Suggested Citation

  • 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).
    • Handle: RePEc:zbw:bonedp:242002
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    References listed on IDEAS

    as
    1. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    2. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    3. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    5. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    6. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    7. 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.
    8. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370, October.
    9. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    11. repec:dau:papers:123456789/5647 is not listed on IDEAS
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    More about this item

    Keywords

    no arbitrage criteria; portfolio constraints; supermartingale measures; bang-bang control;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General

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