Mean-Variance Hedging in Large Financial Markets

We consider a mean-variance hedging (MVH) problem for an arbitrage-free large financial market, that is, a financial market with countably many risky assets modelled by a sequence of continuous semimartingales. By using the stochastic integration theory for a sequence of semimartingales developed in De Donno and Pratelli [6], we extend the results about change of numeraire and MVH of Gourieroux et al. [12] to this setting. We also consider, for all n epsilon 1, the market formed by the first n risky assets and study the solutions to the corresponding n-dimensional MVH problem and their behaviour when n tends to infinity.