Before revision: We generalize the results of Mostovyi (2015) on the problem of optimal investment with intermediate consumption in a general semimartingale setting. We show that the  no unbounded profit with bounded risk condition suffices to establish the key duality relations of utility maximization and , moreover, represents the minimal no-arbitrage-type assumption .
After revision: We generalize the results of Mostovyi (2015) on 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 no unbounded profit with bounded risk condition suffices to establish the key duality relations of utility maximization and , moreover, represents the minimal no-arbitrage-type assumption .