Journal of the
Korean Mathematical Society JKMS

In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be {\it 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 It\^o process, is given.

Keywords: equivalent martingale measure, fair market, allowable strategy, no-arbitrage, replicatable contingent claim, arbitrage pricing, It\^o process

MSC numbers: 60G44, 60H05