Abstract
We consider the 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.
Highlights
A fundamental problem of mathematical finance is that of an investor who wants to invest and consume in a way that maximizes his expected utility
When the consumption occurs only at maturity and the utility function is deterministic a necessary and sufficient condition has been obtained in Kramkov and Schachermayer [18]
In the case of intermediate consumption and stochastic field utility, the latest sufficient conditions are due to Karatzas and Zitkovic [13] and Zitkovic [25]
Summary
A fundamental problem of mathematical finance is that of an investor who wants to invest and consume in a way that maximizes his expected utility. When the consumption occurs only at maturity and the utility function is deterministic a necessary and sufficient condition has been obtained in Kramkov and Schachermayer [18]. It is stated as the finiteness of the dual value function. In the case of intermediate consumption and stochastic field utility, the latest sufficient conditions are due to Karatzas and Zitkovic [13] and Zitkovic [25]. This paper obtains necessary and sufficient conditions in the general framework of an incomplete financial model with a stochastic field utility and intermediate consumption occurring according to some stochastic clock.
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