Robust utility maximisation under proportional transaction costs for c\`adl\`ag price processes

TL;DR

This paper extends robust utility maximisation results to general cglg price processes with transaction costs, providing conditions for optimal strategies in incomplete markets under model uncertainty.

Contribution

It generalizes existing results to broader price processes and filtrations, answering an open question about the necessity of embedding into a countable product space.

Findings

Established existence of optimal trading strategies under new conditions.

Extended the framework from continuous to general cglg processes.

Provided a positive answer to an open question in the literature.

Abstract

We consider robust utility maximisation in continuous-time financial markets with proportional transaction costs under model uncertainty. For this purpose, we work in the framework of Chau and R\'asonyi (2019), where robustness is achieved by maximising the worst-case expected utility over a possibly uncountable class of models that are all given on the same underlying filtered probability space. In this setting, we give sufficient conditions for the existence of an optimal trading strategy, extending the result for utility functions on the positive half-line of Chau and R\'asonyi (2019) from continuous to general strictly positive c\`adl\`ag price processes and from complete to incomplete filtrations. Our result allows us to provide a positive answer to an open question pointed out in Chau and R\'asonyi (2019), and shows that the embedding into a countable product space is not essential.