Before revision: We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by utility stochastic fields. 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: We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. 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.