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December 18, 2006 13:54 Proceedings Trim Size: 9in x 6in ritsumeikan3 Financial Markets with Asymmetric Information
 

Summary: December 18, 2006 13:54 Proceedings Trim Size: 9in x 6in ritsumeikan3
Financial Markets with Asymmetric Information:
Information Drift, Additional Utility and Entropy
Stefan Ankirchner and Peter Imkeller
Institut f¨ur Mathematik, Humboldt-Universit¨at zu Berlin,
Unter den Linden 6, 10099 Berlin, Germany
We review a general mathematical link between utility and infor-
mation theory appearing in a simple financial market model with
two kinds of small investors: insiders, whose extra information
is stored in an enlargement of the less informed agents' filtration.
The insider's expected logarithmic utility increment is described
in terms of the information drift, i.e. the drift one has to eliminate
in order to perceive the price dynamics as a martingale from his
perspective. We describe the information drift in a very general
setting by natural quantities expressing the conditional laws of the
better informed view of the world. This on the other hand allows to
identify the additional utility by entropy related quantities known
from information theory.
Key words: enlargement of filtration; logarithmic utility; utility
maximization; heterogeneous information; insider model; Shannon

  

Source: Ankirchner, Stefan - Institut für Angewandte Mathematik, Universität Bonn

 

Collections: Mathematics