We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a  semi-static utility maximization for the case of exponential utility preference. The randomization techniques recently developed in BDT17 allow us to transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space. Using the one-period duality result in bartl2016exponential, together with measurable selection arguments and minimax theorem, we are able to prove all together the existence of the optimal strategy , convex duality theorem as well as the auxiliary dynamic programming principle in our context with transaction costs. As\hspace{0pt}%DIFAUXCMD to a weaker market condition. Moreover, as } an application of the duality representation, some important features of utility indifference prices are investigated in the robust setting .
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization techniques recently developed in BDT17 allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in bartl2016exponential, we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in \mbox{%DIFAUXCMD bartl2016exponential\hspace{0pt}%DIFAUXCMD to a weaker market condition. Moreover, as } an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs .
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