Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 90A09 Finance, portfolios, investment
- 90A10 Utility theory
- 90D44 Games involving topology or set theory

**Résumé:** In this paper we consider an investor who trades in a complete financial
market so as to maximize his expected utility of wealth at a prespecified
time. We assume that he is in the following position : His portfolio
decisions are based on a public information flow but he possesses extra
information about the law of some functional of the future prices of a
stock. Our basic question is then: How should he trade on the financial
market to optimally exploit his extra information? We show that the optimal
trading strategies corresponding to a such investor (called weakly informed)
are derived from processes which are solutions of what we called in a
previous paper a conditioned stochastic differential equation. Such
processes can be realized as all the possible filters of the price process
seen under the martingale probability measure but looked in a enlarged
filtration. This filtering makes the link with the works of several authors
who considered financial markets in which one insider possesses from the
beginning extra information about the outcome $\omega $ by $\omega $ of some
variable (this is a higher information level which we call strong).

**Mots Clés:** *Conditioned stochastic differential equation ; Filtering ; Utility
maximization ; Portfolio optimization ; Burger's equation*

**Date:** 2001-05-07

**Prépublication numéro:** *PMA-654*

**Pdf file : **PMA-654.pdf