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.
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 |