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

TL;DR

This paper establishes that the finiteness of value functions in primal and dual problems is both necessary and sufficient for the core results of optimal investment with intermediate consumption in incomplete markets.

Contribution

It provides a precise characterization of conditions under which the fundamental theorems of asset pricing hold in complex market models.

Findings

Finiteness of primal and dual value functions is essential.

Necessary and sufficient condition for key assertions.

Applicable to incomplete semimartingale models.

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