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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.

Suggested Citation

  • Elyès Jouini, 2001. "Arbitrage and investment opportunities," Finance and Stochastics, Springer, vol. 5(3), pages 305-325.
  • 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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    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, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    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. Jouini, Elyes & Napp, Clotilde & Schachermayer, Walter, 2005. "Arbitrage and state price deflators in a general intertemporal framework," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 722-734, September.
    5. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    6. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, 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.
    8. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.
    9. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    10. 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, vol. 2(4), pages 327-355, October.

    More about this item

    Keywords

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

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G19 - Financial Economics - - General Financial Markets - - - Other

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