A remark on arbitrage and martingale measure
type: Item
instance of: scholarly article
title: A remark on arbitrage and martingale measure
zbMATH Open document ID: 0807.90009
author: Shigeo Kusuoka
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-03-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 548930
zbMATH Keywords: option pricing
zbMATH Keywords: absence of arbitrage
zbMATH Keywords: Mackey topology
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: existence of an equivalent martingale measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195166576
OpenAlex ID: W2076907650
cites work: Equivalent martingale measures and no-arbitrage in stochastic securities market models
cites work: REPRESENTING MARTINGALE MEASURES WHEN ASSET PRICES ARE CONTINUOUS AND BOUNDED
cites work: ARBITRAGE AND FREE LUNCH WITH BOUNDED RISK FOR UNBOUNDED CONTINUOUS PROCESSES
cites work: A general version of the fundamental theorem of asset pricing
cites work: Martingales and arbitrage in multiperiod securities markets
cites work: A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time
cites work: MARTINGALE MEASURES FOR DISCRETE‐TIME PROCESSES WITH INFINITE HORIZON
cites work: Arbitrage et lois de martingale. (Arbitrage and martingale laws)
cites work: Q3866824
cites work: Q3669960
DOI: 10.2977/PRIMS/1195166576
description: scientific article; zbMATH DE number 548930