Before revision:  Our main result establishes existence of the optimal trading strategies in such markets under no smoothness requirements on the utility function , and relates them to the corresponding dual objects. Moreover, we show that the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.
After revision:  Our main result establishes existence of the optimal trading strategies in such markets under no smoothness requirements on the utility function . The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.