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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Mean-variance hedging in large financial markets


Code(s) de Classification MSC:

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)