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)...

We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constraint to lie in a closed convex domain...