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
- 60H05 Stochastic integrals
- 60G48 Generalizations of martingales

**Résumé:** We consider a mean-variance hedging problem for an arbitrage-free large
financial market, i.e. a financial market with countably many risky assets
modelled by a sequence of continuous semimartingales. By using the
stochastic integration theory for cylindrical martingales developed in
Mikulevicius and Rozovskii (1998), we extend the results about change of num%
\'{e}raire and mean-variance hedging of Gourieroux, Laurent and Pham (1998)
to this setting. We also consider, for all $n\geq 1$, the market formed by
the first $n$ risky assets and study the solutions to the $n$-dimensional
mean-variance hedging problem associated and their behaviour when $n$ tends
to infinity.

**Mots Clés:** *hedging ; large financial market ; cylindrical martingales ;
normalized stochastic integral ; numéraire ; artificial extension method*

**Date:** 2002-10-02

**Prépublication numéro:** *PMA-758*

**Pdf file : **PMA-758.pdf

**Second version : ** PMA_758Bis.pdf (8 sept 2003)