Asymptotics of robust utility maximization

TL;DR

This paper studies the long-term behavior of robust utility maximization in stochastic factor models, characterizing optimal strategies and worst-case scenarios through ergodic control and duality methods.

Contribution

It introduces a duality framework for analyzing robust utility maximization, linking it to risk-sensitive control and ergodic Bellman equations for the first time.

Findings

Characterizes the optimal growth rate of robust utility.

Identifies optimal long-term trading strategies.

Determines asymptotic worst-case models.

Abstract

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\lambda\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.