Delbaen, Freddy and Schachermayer, Walter (1999) The fundamental theorem of asset pricing for unbounded stochastic processes. Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science", 24. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.

PDF
Download (377Kb)  Preview 
Abstract
The Fundamental Theorem of Asset Pricing states  roughly speaking  that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingale measure for S. It turns out that it is quite hard to give precise and sharp versions of this theorem in proper generality, if one insists on modifying the concept of "no arbitrage" as little as possible. It was shown in [DS94] that for a locally bounded R^dvalued semimartingale S the condition of No Free Lunch with Vanishing Risk is equivalent to the existence of an equivalent local martingale measure for the process S. It was asked whether the local boundedness assumption on S may be dropped. In the present paper we show that if we drop in this theorem the local boundedness assumption on S the theorem remains true if we replace the term equivalent local martingale measure by the term equivalent sigmamartingale measure. The concept of sigmamartingales was introduced by Chou and Emery  under the name of "semimartingales de la classe (Sigma_m)". We provide an example which shows that for the validity of the theorem in the non locally bounded case it is indeed necessary to pass to the concept of sigmamartingales. On the other hand, we also observe that for the applications in Mathematical Finance the notion of sigmamartingales provides a natural framework when working with non locally bounded processes S. The duality results which we obtained earlier are also extended to the non locally bounded case. As an application we characterize the hedgeable elements. (author's abstract)
Item Type:  Paper 

Divisions:  Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes Departments > Finance, Accounting and Statistics > Statistics and Mathematics Departments > Marketing > Service Marketing und Tourismus Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft 
Depositing User:  Repository Administrator 
Date Deposited:  08 Mar 2002 09:10 
Last Modified:  28 Mar 2015 01:13 
URI:  http://epub.wu.ac.at/id/eprint/850 
Actions
View Item 