A remark on arbitrage and martingale measure
Summary: In the option pricing theory the most important fact is that the absence of arbitrage follows from the existence of equivalent martingale measure for the price process of securities. There are several attempts to show the converse statement that the absence of arbitrage implies the existence of an equivalent martingale measure. In the discrete time case, the proof for the most general case has been given by Dalang-Morton- Willinger and Schachermayer. On the continuous time case Stricker gave beautiful results, and they were extended by Delbaen, Schachermayer and Delbaen-Schachermayer. In particular, the Mackey topology was clearly used by Delbaen, and his result is quite satisfactory in the case where price processes are pathwise continuous. In this paper, we give some remarks on Orlicz spaces, Mackey topologies, and results by \textit{J.-P. Ansel} and \textit{C. Stricker} [Lect. Notes Math. 1426, 266-274 (1990; Zbl 0701.60041)] and \textit{F. Delbaen} [Math. Finance 2, 107-130 (1992)]. Then we give a certain necessary and sufficient conditions for the existence of an equivalent martingale measure.
existence of an equivalent martingale measure
scientific article; zbMATH DE number 548930