  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 nondominated probabilistic models of her endowment by
dynamically investing in a financial market, and statically in available
options. 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 (calibrated) martingale measures holds true, and
that the problem satisfies the dynamic programming principle (in case of no
options). Further it is shown that the value of the utility maximization
problem converges to the robust superhedging price as the risk aversion
parameter gets large, and examples of nondominated probabilistic models are
discussed.
