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Arbitrage and Investment Opportunities

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  • Elyès Jouini

    (Crest)

  • Clotilde Napp

    (Crest)

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 Centre de Recherche en Economie et Statistique in its series Working Papers with number 98-29.

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Date of creation: 1998
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Handle: RePEc:crs:wpaper:98-29

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Cited by:
  1. Clotilde Napp & Elyès Jouini, 2005. "Arbitrage and state price deflators in a general intertemporal framework," Post-Print halshs-00151526, HAL.
  2. M A H Dempster & I V Evstigneev & M I Taksar, 2005. "Asset pricing and hedging in financial markets with transaction costs: an approach based on the von Neumann-Gale model," Working Papers 062005, University of Cambridge, Judge Business School, Centre for Financial Research.
  3. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
  4. 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.
  5. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
  6. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
  7. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.

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