Duality theory for robust utility maximisation

In this paper, we present a duality theory for the robust utility maximisation problem in continuous time functions defined on positive real line. Our results are inspired by – and can be seen as analogues of seminal work Kramkov Schachermayer (Ann. Appl. Probab. 9:904–950, 1999). Namely, show that if set attainable trading outcomes pricing measures satisfy bipolar relation, then is with conjugate problem. We further discuss existence optimal strategies. particular, our general include case logarithmic power utility, they apply to drift volatility uncertainty.