Before revision:  By building on the results of Mostovyi (2015), we show that the key duality relations of the utility maximization theory hold under the minimal assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.
After revision:  By building on the results of Mostovyi (2015), we show that the key duality relations of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.