Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption

Abstract

We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finite

arXiv commentIn this version the no-arbitrage assumption is changed from M\neq \emptyset, where M denotes the set of locally equivalent martingale measures, to Z\neq \emptyset, where Z denotes the set of equivalent martingale deflators