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We consider a discrete time financial market with proportional transactioncosts under model uncertainty, and study a num\'eraire-based semi-staticutility maximization problem with an exponential utility preference. Therandomization techniques recently developed in \cite{BDT17} allow us totransform the original problem into a frictionless counterpart on an enlargedspace. By suggesting a different dynamic programming argument than in\cite{bartl2016exponential}, we are able to prove the existence of the optimalstrategy and the convex duality theorem in our context with transaction costs.In the frictionless framework, this alternative dynamic programming argumentalso allows us to generalize the main results in \cite{bartl2016exponential} toa weaker market condition. Moreover, as an application of the dualityrepresentation, some basic features of utility indifference prices areinvestigated in our robust setting with transaction costs.

Utility maximization with proportional transaction costs under model uncertainty