Utility Maximization under Model Uncertainty in Discrete Time

TL;DR

This paper formulates a general utility maximization problem considering model uncertainty in discrete time, establishing conditions for the existence of optimal portfolios across different utility functions.

Contribution

It introduces a comprehensive framework for utility maximization under nondominated model uncertainty in discrete time, including existence results and conditions for unbounded utilities.

Findings

Optimal portfolios exist for bounded utility functions.

Integrability conditions are necessary for unbounded utility functions.

Nonexistence can occur even with finite value functions without these conditions.

Abstract

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value function is finite.