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Additional logarithmic utility of an insider

Jürgen Amendinger, Peter Imkeller and Martin Schweizer

No 1998,25, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information flow, the insider possesses from the beginning extra information about the outcome of some random variable G, e.g., the future price of a stock. We solve the two optimization problems explicitly and rewrite the insider's additional expected logarithmic utility in terms of a relative entropy. This allows us to provide simple conditions on G for the finiteness of this additional utility and to show that it is basically given by the entropy of G.

Keywords: insider trading; entropy; utility maximization; initial enlargement of filtrations; relative entropy (search for similar items in EconPapers)
Date: 1998
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