  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.
