No arbitrage condition for positive diffusion price processes
type: Item
instance of: scholarly article
title: No arbitrage condition for positive diffusion price processes
zbMATH Open document ID: 1074.91014
DOI: 10.1023/A:1024173029378
author: Freddy Delbaen
author: Hiroshi Shirakawa
published in: Asia-Pacific Financial Markets
publication date: 2004-02-03T00:00:00Z
review text: At first, the authors present local martingale analysis. More exactly, they consider Markovian local martingale process \(X\) without drift and analyse when this process will reach the origin. For this purpose the construction of the weak solution by means of the method of time changes is used. Then with the help of the Ray-Knight theorem the necessary and sufficient condition for \(X\) to reach the origin is established. Afterwards, the equation is transformed and the criterion is stated when \(X\) is a genuine martingale. These results are used to solve the problem when a nonnegative diffusion process admits an equivalent martingale measure. So, the existence of an equivalent local martingale measure for the general Markovian stock price model is established.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 2036993
zbMATH Keywords: equivalent martingale measure
zbMATH Keywords: arbitrage
zbMATH Keywords: Ray-Knight theorem
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: a:1024173029378
OpenAlex ID: W30805069
description: scientific article; zbMATH DE number 2036993