  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.
