Robust utility maximization with nonlinear continuous semimartingales

TL;DR

This paper addresses a robust utility maximization framework in continuous time, accounting for model uncertainty modeled by nonlinear continuous semimartingales with uncertain local characteristics, establishing duality and existence results.

Contribution

It introduces a duality approach for robust utility maximization under nonlinear semimartingale models with uncertain local characteristics, and proves existence of optimal portfolios.

Findings

Duality between utility maximization and a conjugate problem

Existence of optimal portfolios for various utility functions

Framework accommodating model uncertainty via set-valued local characteristics

Abstract

In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function that depends on time and path. We show that the robust utility maximization problem is in duality with a conjugate problem, and we study the existence of optimal portfolios for logarithmic, exponential and power utilities.