Optimal communication to a group often entails a trade-off between precision of information conveyed and common understanding (or approximate common knowledge) of the information within the group. We argue that an understanding of this trade-off is central in many contexts, including central bank communication and the design of accounting standards, as well as understanding the design of langua...

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 risk-free numéraire is not assumed. Probabilistic dual representations are obtained for the bid and ask prices of such opt...