  We consider a multivariate financial market with transaction costs and study
the problem of finding the minimal initial capital needed to hedge, without
risk, European-type contingent claims. The model is similar to the one
considered in Bouchard and Touzi (2000), except that some of the assets can be
exchanged freely, i.e. without paying transaction costs. In this context, we
generalize the result of the above paper and prove that the value of this
stochastic control problem is given by the cost of the cheapest hedging
strategy in which the number of non-freely exchangeable assets is kept constant
over time.
