# Duality Theory for Robust Utility Maximisation

arXiv: https://arxiv.org/abs/2007.08376 · HTML: https://mlsanity.com/paper/2007.08376/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)

## Abstract (arXiv)

In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.