Robust utility maximisation under proportional transaction costs for cà dlà g price processes

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 Rásonyi (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 Rásonyi (2019) from continuous to general strictly positive cà dlà g 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 Rásonyi (2019), and shows that the embedding into a countable product space is not essential.