Explicit characterization of the super-replication strategy in financial markets with partial transaction costs

We consider a continuous time multivariate financial market with proportional 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. This is the so-called non-effcient friction case. To our knowledge, this is the first time that such a model is considered in a continuous time setting. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time.