Journal of the Korean Mathematical Society (대한수학회지)
- Volume 35 Issue 3
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- Pages.659-673
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- 1998
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
A NEW LOOK AT THE FUNDAMENTAL THEOREM OF ASSET PRICING
Abstract
In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be fair if there exists an equivalent martingale measure for the price process, deflated by a numeraire asset. It is shown that the fairness of a market is invariant under the change of numeraire. As a consequence, we show that the characterization of the fairness of a market is reduced to the case where the deflated price process is bounded. In the latter case a theorem of Kreps (1981) has already solved the problem. By using a theorem of Delbaen and Schachermayer (1994) we obtain an intrinsic characterization of the fairness of a market, which is more intuitive than Kreps' theorem. It is shown that the arbitrage pricing of replicatable contingent claims is independent of the choice of numeraire and equivalent martingale measure. A sufficient condition for the fairness of a market, modeled by an Ito process, is given.
Keywords
- equivalent martingale measure;
- fair market;
- allowable strategy;
- no-arbitrage;
- replicatable contingent claim;
- arbitrage pricing;
- Ito process