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We consider simple models of financial markets with less and better
informed investors described by a smaller and a larger filtration on a
general stochastic basis that describes the market dynamics, including
continuous and jump components. We study the relation between different forms of non existance of arbitrage and the characteristics of the stochastic basis under the different filtrations. This is achieved through the analysis of the properties of the numéraire portfolio. Furthermore, we focus on the problem of calculating the additional logarithmic utility of the better informed investor in terms of the Shannon antropy of is additional information. The information drift, i.e. the drift to eliminate in order to preserved the martingale property in the larger filtration terms out to be the crucial quantity needed to tackle these problems. We show that the expected
ed logarithmic utility increment due to better information equals its Shannon
entropy also in case of a pure jump basis with jumps that are quadratically
hedgeable, and so extend a similar result known for bases consisting of
continuous semimartingales. An example illustrates that the equality may
not persist if both continuous and jump components are present in the
underlying.