Additional Utility of Insiders with Imperfect Dynamical Information

UPF Economics and Business Working Paper No. 675

28 Pages Posted: 8 Sep 2003

See all articles by José Manuel Corcuera

José Manuel Corcuera

University of Barcelona - Faculty of Mathematics

Peter Imkeller

Humboldt University of Berlin - Department of Mathematics

Arturo Kohatsu-Higa

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

David Nualart

University of Barcelona - Department of Statistics

Date Written: April 4, 2003

Abstract

In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every trader. Our financial markets are based on Wiener space. In probabilistic terms we obtain an infinite dimensional extension of Jacod's theorem to cover cases of progressive enlargement of filtrations. The application of this result gives the semimartingale decomposition of the original Wiener process under the progressively enlarged filtration. As an application we prove that if the rate at which the additional noise in the insider's information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.

Keywords: Insider trading, enlargement of filtrations, Malliavin's calculus, utility maximization, arbitrage

JEL Classification: G140

Suggested Citation

Corcuera Valverde, José Manuel and Imkeller, Peter and Kohatsu-Higa, Arturo and Nualart, David, Additional Utility of Insiders with Imperfect Dynamical Information (April 4, 2003). UPF Economics and Business Working Paper No. 675, Available at SSRN: https://ssrn.com/abstract=428203 or http://dx.doi.org/10.2139/ssrn.428203

José Manuel Corcuera Valverde

University of Barcelona - Faculty of Mathematics ( email )

Gran Via de les Corts
Catalanes 585
Barcelona 08007
Spain

Peter Imkeller

Humboldt University of Berlin - Department of Mathematics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Arturo Kohatsu-Higa (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-93) 542 27 50 (Phone)
(34-93) 542 17 46 (Fax)

David Nualart

University of Barcelona - Department of Statistics ( email )

Barcelona
Spain
+34-934021656 (Phone)
+34-934021601 (Fax)

HOME PAGE: http://www.mat.ub.es/~nualart/

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