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The numéraire portfolio, asymmetric information and entropy

Please always quote using this URN:urn:nbn:de:0296-matheon-7241
  • 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.

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Metadaten
Author:Peter Imkeller, Evangelia Petrou
URN:urn:nbn:de:0296-matheon-7241
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/11/10
Release Date:2010/08/10
Institute:Humboldt-Universität zu Berlin
Preprint Number:734
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