We consider a problem of optimal investment with intermediate consumption andrandom endowment in an incomplete semimartingale model of a financial market.We establish the key assertions of the utility maximization theory assumingthat both primal and dual value functions are finite in the interiors of theirdomains as well as that random endowment at maturity can be dominated by theterminal value of a self-financing wealth process. In order to facilitateverification of these conditions, we present alternative, but equivalentconditions, under which the conclusions of the theory hold.
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