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The background for the general mathematical link between utility andinformation theory investigated in this paper is a simple financial marketmodel 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 differenceof the insider's and the less informed trader's expected logarithmic utility isdescribed in terms of the information drift, that is, the drift one has toeliminate in order to perceive the price dynamics as a martingale from theinsider's perspective. On the one hand, we describe the information drift in avery general setting by natural quantities expressing the probabilistic betterinformed view of the world. This, on the other hand, allows us to identify theadditional utility by entropy related quantities known from information theory.In particular, in a complete market in which the insider has some fixedadditional information during the entire trading interval, its utilityincrement can be represented by the Shannon information of his extra knowledge.For general markets, and in some particular examples, we provide estimates ofmaximal utility by information inequalities.

The Shannon information of filtrations and the additional logarithmic utility of insiders