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

We consider a continuous time multivariate financial market with proportionaltransaction costs and study the problem of finding the minimal initialcapital needed to hedge, without risk, European-type contingent claims. Themodel is similar to the one considered in Bouchard and Touzi (2000) exceptthat some of the assets can be exchanged freely, i.e. without paying transactioncosts. This is the so-called non-efficient friction case. To our knowledge, thisis 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 thesuper-replication price is given by the cost of the cheapest hedging strategyin which the number of non-freely exchangeable assets is kept constant overtime.