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:**

- 60G44 Martingales with continuous parameter
- 60G55 Point processes
- 60H07 Stochastic calculus of variations and the Malliavin calculus
- 60J60 Diffusion processes, See also {58G32}
- 60J75 Jump processes
- 90A09 Finance, portfolios, investment
- 90A35 Informational economics

**Résumé:** We define and study the notion of static and dynamic weak
anticipation in financial markets, both complete and incomplete. We compute
the minimal gain in utility provided by such information and characterize a
minimal associated probability measure. It is remarkable that this
probability is independent of the utility function used by the trader both
in the static and dynamic case.

**Mots Clés:** *Portfolio optimization ; Incomplete markets ; Weak information ;
Weak information flow ; Additional utility ; Conditioned stochastic
differential equation ; Dynamic conditioning ; Schrödinger processes*

**Date:** 2002-05-06

**Prépublication numéro:** *PMA-724*

**Pdf file :** PMA-724.pdf