Optimal investment with intermediate consumption under no unbounded profit with bounded risk

TL;DR

This paper investigates optimal investment strategies with intermediate consumption in incomplete markets, demonstrating that classical utility maximization results hold under the NUPBR condition and finite value functions.

Contribution

It extends utility maximization theory to models satisfying NUPBR, ensuring the key results remain valid in more general incomplete market settings.

Findings

Utility maximization results hold under NUPBR.

Finiteness of primal and dual value functions is crucial.

Key conclusions of utility theory are preserved.

Abstract

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.