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March 2006 The Shannon information of filtrations and the additional logarithmic utility of insiders
Stefan Ankirchner, Steffen Dereich, Peter Imkeller
Ann. Probab. 34(2): 743-778 (March 2006). DOI: 10.1214/009117905000000648


The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed traders and insiders, whose extra information is represented by an enlargement of the other agents’ filtration. The expected logarithmic utility increment, that is, the difference of the insider’s and the less informed trader’s expected logarithmic utility is described in terms of the information drift, that is, the drift one has to eliminate in order to perceive the price dynamics as a martingale from the insider’s perspective. On the one hand, we describe the information drift in a very general setting by natural quantities expressing the probabilistic better informed view of the world. This, on the other hand, allows us to identify the additional utility by entropy related quantities known from information theory. In particular, in a complete market in which the insider has some fixed additional information during the entire trading interval, its utility increment can be represented by the Shannon information of his extra knowledge. For general markets, and in some particular examples, we provide estimates of maximal utility by information inequalities.


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Stefan Ankirchner. Steffen Dereich. Peter Imkeller. "The Shannon information of filtrations and the additional logarithmic utility of insiders." Ann. Probab. 34 (2) 743 - 778, March 2006.


Published: March 2006
First available in Project Euclid: 9 May 2006

zbMATH: 1098.60065
MathSciNet: MR2223957
Digital Object Identifier: 10.1214/009117905000000648

Primary: 60H30 , 94A17
Secondary: 60G44 , 91B16

Keywords: differential entropy , Enlargement of filtration , Entropy , heterogeneous information , information difference , insider model , logarithmic utility , Shannon information , utility maximization

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 2 • March 2006
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