Super-Replication with Fixed Transaction Costs

We study super–replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market models the super–replication price is prohibitively costly and leads to trivial buy–and–hold strategies. Our second result derives nontrivial scaling limits of super–replication prices for binomial models with small fixed costs.