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Arbitrage and investment opportunities

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  • Elyès Jouini

    ()
    (CREST-ENSAE, 15, Bd Gabriel Péri, 92241 Malakoff Cedex, France and CERMSEM-Université de Paris I, France and Stern School of Business at NYU, 44 W 4th St, NY, USA CREST-ENSAE , and Université Paris IX-Dauphine, France Manuscript)

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

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 5 (2001)
Issue (Month): 3 ()
Pages: 305-325

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Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:305-325

Note: received: December 1998; final version received: June 2000
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Related research

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

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Cited by:
  1. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
  2. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, Springer, vol. 15(1), pages 57-83, January.
  3. Elyès Jouini, 2001. "Arbitrage and Control Problems in Finance. Presentation," Post-Print halshs-00167152, HAL.
  4. 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, University of Cambridge, Judge Business School, Centre for Financial Research 062005, University of Cambridge, Judge Business School, Centre for Financial Research.
  5. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
  6. Clotilde Napp & Elyès Jouini, 2005. "Arbitrage and state price deflators in a general intertemporal framework," Post-Print halshs-00151526, HAL.
  7. 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.

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