  Duality for robust hedging with proportional transaction costs of path
dependent European options is obtained in a discrete time financial market with
one risky asset. Investor's portfolio consists of a dynamically traded stock
and a static position in vanilla options which can be exercised at maturity.
Both the stock and the option trading is subject to proportional transaction
costs. The main theorem is duality between hedging and a Monge-Kantorovich type
optimization problem. In this dual transport problem the optimization is over
all the probability measures which satisfy an approximate martingale condition
related to consistent price systems in addition to the usual marginal
constraints.
