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 pricesof such options, together with constructions of hedging strategies , optimal stopping times and approximate martingale representations for both long and short option positions  .
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 is subject to proportional transaction costs, and where the existence of a risk-free num\'eraire is not assumed. Constructions leading to algorithms for computing the prices, optimal hedging strategies and stopping times are presented for both long and short option positions in this setting, together with probabilistic (martingale) representations for the option prices .
D
in all assets
R
riskfree numeraire
risk-free num\'eraire
R
Probabilistic dual representations are obtained for the bid and ask pricesof such options, together with constructions of hedging strategies , optimal stopping times and approximate martingale representations
Constructions leading to algorithms for computing the prices, optimal hedging strategies and stopping times are presented
A
in this setting, together with probabilistic (martingale) representations for the option prices