Before revision:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
After revision:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all "admissible" wealth processes, for the stopped model S^{\tau}.