Explicit solution of the multivariate super - replicationproblem under transaction costs

We consider a multivariate nancial market with transaction costs as in Kabanov (1999). We study the problem of nding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this sto-chastic control problem is given by the cost of the cheapest buy-and-hold strategy. This is an extension of the already known result in the one-dimensional case. An important feature of our analysis is that we do not make use of the dual formulation of the problem, as in the previous literature. We are grateful to Professor Yuri Kabanov for a careful reading of this paper which considerably improved its presentation. y This work was achieved while the author was aaliated to CEREMADE (Universitt Paris Dauphine) and CREST.