Exponential utility maximization under model uncertainty for unbounded endowments

We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of non-dominated probabilistic models of her endowment by dynamically investing in a financial market. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of martingale measures holds true, and that the problem satisfies the dynamic programming principle.