Arbitrage and investment opportunities
AbstractWe 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 noarbitrage condition in these imperfect models, from which it is easy to derive pricing formulae for contingent claims.
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Date of creation: 01 Jun 2001
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Publication status: Published, Finance and Stochastics, 2001, 5, 3, 305-325
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Arbitrage; investment opportunities; numéraire; market frictions; Yan's Theorem.;
Other versions of this item:
- Elyès Jouini & Clotilde Napp, 1998. "Arbitrage and Investment Opportunities," Working Papers 98-29, Centre de Recherche en Economie et Statistique.
- Elyès Jouini & Clotilde Napp, 1999. "Arbitrage and Investment Opportunities," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-034, New York University, Leonard N. Stern School of Business-.
- 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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