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Arbitrage and investment opportunities

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  • Jouini, Elyès
  • Napp, Clotilde
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    Abstract

    We consider a model in which any investment opportunity is described in terms of cash flows. We don't assume that there is a numéraire, enabling investors to transfer wealth through time; the time horizon is not supposed to be finite and the investment opportunities are not specifically related to the buying and selling of securities on a financial market. In this quite general framework, we show that the assumption of no-arbitrage is essentially equivalent to the existence of a "discount process" under which the "net present value" of any available investment is nonpositive. Since most market imperfections, such as short sale constraints, convex cone constraints, proportional transaction costs, no borrowing or different borrowing and lending rates, etc., can fit in our model for a specific set of investments, we then obtain a characterization of the no-arbitrage condition in these imperfect models, from which it is easy to derive pricing formulae for contingent claims.

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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/5591.

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    Date of creation: Jul 2001
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    Publication status: Published in Finance and Stochastics, 2001, Vol. 5, no. 3. pp. 305-325.Length: 20 pages
    Handle: RePEc:dau:papers:123456789/5591

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    Related research

    Keywords: Arbitrage; investment opportunities; numéraire; market frictions; Yan's Theorem;

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    Cited by:
    1. Clotilde Napp & Elyès Jouini, 2005. "Arbitrage and state price deflators in a general intertemporal framework," Post-Print, HAL halshs-00151526, HAL.
    2. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, Springer, vol. 15(1), pages 57-83, January.
    3. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    4. 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, Springer, vol. 2(4), pages 327-355, October.
    5. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print, HAL halshs-00703138, HAL.

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