Optimal investment with intermediate consumption and random endowment

TL;DR

This paper develops a utility maximization framework for optimal investment with intermediate consumption and random endowment in incomplete markets, establishing key theoretical assertions under broad conditions.

Contribution

It introduces new equivalent conditions that ensure the validity of utility maximization theory in complex financial models with random endowments.

Findings

Established finiteness of primal and dual value functions under broad conditions

Provided alternative conditions for verifying key assumptions

Extended utility maximization theory to incomplete semimartingale models

Abstract

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