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Investment and Arbitrage Opportunities with Short Sales Constraints

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  • Laurence Carassus
  • Elyès Jouini

Abstract

In this paper we consider a family of investment projects defined by their deterministic cash flows. We assume stationarity—that is, projects available today are the same as those available in the past. In this framework, we prove that the absence of arbitrage opportunities is equivalent to the existence of a discount rate such that the net present value of all projects is nonpositive if the projects cannot be sold short and is equal to zero otherwise. Our result allows for an infinite number of projects and for continuous as well as discrete cash flows, generalizing similar results established by Cantor and Lippman (1983, 1995) and Adler and Gale (1997) in a discrete time framework and for a finite number of projects.

Suggested Citation

  • Laurence Carassus & Elyès Jouini, 1998. "Investment and Arbitrage Opportunities with Short Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 169-178, July.
    • Handle: RePEc:bla:mathfi:v:8:y:1998:i:3:p:169-178
    DOI: 10.1111/1467-9965.00051
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    Cited by:

    1. Carassus, Laurence & Jouini, Elyes, 2000. "A discrete stochastic model for investment with an application to the transaction costs case," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 57-80, February.
    2. Elyès Jouini, 2003. "Market imperfections , equilibrium and arbitrage," Post-Print halshs-00167131, HAL.
    3. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    4. David M. Schizer & Michael R. Powers & Martin Shubik, 2003. "Market Bubbles and Wasteful Avoidance: Tax and Regulatory Constraints on Short Sales," Yale School of Management Working Papers ysm356, Yale School of Management.
    5. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    6. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    7. repec:dau:papers:123456789/5590 is not listed on IDEAS

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