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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/26970
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| Title: | Arbitrage and Investment Opportunities |
| Authors: | Jouini, Elyès
Napp, Clotilde |
| Keywords: | arbitrage
investment opportunities
numeraire
market imperfections
transaction costs
Yan`s theorem |
| Issue Date: | Sep-1999 |
| Series/Report no.: | FIN-99-034 |
| Abstract: | We consider a model in which all investment opportunities are described
in terms of cash flows. We don't assume that there is a
numéraire, the time horizon is not supposed to be finite, 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 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. Compared with existing results, our approach allows to consider
markets with no numéraire or with a numéraire that is
subject to constraints. Besides, we introduce a notion of no-free lunch
which is less restrictive than the usual one. Last, we characterize the
assumption of no-arbitrage (or no-free lunch) for more general
investment opportunities, which enables us to consider investments that
are not necessarily related to a market model and, more interestingly,
to generalize the results obtained for imperfect markets and to obtain
them all in a unified way. |
| URI: | http://hdl.handle.net/2451/26970 |
| Appears in Collections: | Finance Working Papers
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