Utility maximization with proportional transaction costs under model uncertainty.

Summary 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 [12] 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 [3], 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 an application of the duality representation, some important features of utility indifference prices are investigated in the robust setting.