Before revision:  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 show that the key duality relations of the utility maximization theory hold under the minimal assumptions of 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 .