Free lunch and arbitrage possibilities in a financial market model with an insider.
type: Item
instance of: scholarly article
title: Free lunch and arbitrage possibilities in a financial market model with an insider.
zbMATH Open document ID: 1047.60041
DOI: 10.1016/S0304-4149(00)00071-5
author: P. Imkeller
author: Monique Pontier
author: Ferenc Weisz
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: The paper studies filtrations on a Wiener space, enlarged by a random variable \(L\) which depends on the whole Brownian motion trajectory. The prototypical example is the supremum of a Wiener process on an interval. The theory is aimed at solving the portfolio problem of an investor who is informed about \(L\), in addition to the usual knowledge of the price process statistics under the original Wiener filtration. The paper looks for the conditions under which the enlarged filtration preserves the semimartingale property of the price process. These conditions are obtained in terms of the conditional law of \(L\) given the original filtration, by means of a measure-valued Malliavin calculus technique. In particular, the probability change that makes the price process a Wiener one under the enlarged filtration is determined by the Radon-Nikodym derivative of the conditional law of \(L\) with respect to this conditional law. Among other things, the authors give conditions under which the relative entropy of the conditional law of \(L\) with respect to the law of \(L\) is finite and positive. They also prove that their prototypical \(L\) generates an asset market model with arbitrage possibilities.
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 2102378
zbMATH Keywords: enlargement of filtrations
zbMATH Keywords: informed investor
zbMATH Keywords: arbitrage
zbMATH Keywords: Malliavin calculus
reviewed by: Alexis Derviz
MaRDI profile type: Publication
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Wikidata QID: Q127977215
full work available at URL: s0304-4149(00)00071-5
OpenAlex ID: W2143296890
description: scientific article; zbMATH DE number 2102378