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Finite utility on financial markets with asymmetric information and the theorem of Bichteler-Dellacherie-Mokobodsky

Please always quote using this URN:urn:nbn:de:0296-matheon-474
  • We consider financial markets with two kinds of small traders: regular traders who perceive the asset price process S through its natural filtration, and insid- ers who possess some information advantage which makes the filtrations through which they perceive the evolution of the market richer. The basic question we dis- cuss is the link between (NFLVR), the semimartingale property of S viewed from the agent’s perspective, and bounded expected utility. We show that whenever an agent’s expected utility is finite, S is a semimartingale with a Doob-Meyer decomposition featuring a martingale part and an information drift. The ex- pected utility gain of an insider with respect to a regular trader is calculated in a completely general setting. In particular, for the logarithmic utility function, utility gain is a function of the relative information drift alone, regardless of the completeness of the market.

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Metadaten
Author:Stefan Ankirchner, Peter Imkeller
URN:urn:nbn:de:0296-matheon-474
Referee:Anton Bovier
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/01/19
Release Date:2004/01/15
Preprint Number:44
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