The pricing and hedging of a general class of options (including American,
Bermudan and European options) on multiple assets are studied in the context of
currency markets where trading in all assets is subject to proportional
transaction costs, and where the existence of a riskfree numeraire is not
assumed. Probabilistic dual representations are obtained for the bid and ask
prices of such options, together with constructions of hedging strategies,
optimal stopping times and approximate martingale representations for both long
and short option positions.