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We consider the robust exponential utility maximization problem in discretetime: An investor maximizes the worst case expected exponential utility withrespect to a family of nondominated probabilistic models of her endowment bydynamically investing in a financial market, and statically in availableoptions. We show that, for any measurable random endowment (regardless ofwhether the problem is finite or not) an optimal strategy exists, a dualrepresentation in terms of (calibrated) martingale measures holds true, andthat the problem satisfies the dynamic programming principle (in case of nooptions). Further it is shown that the value of the utility maximizationproblem converges to the robust superhedging price as the risk aversionparameter gets large, and examples of nondominated probabilistic models arediscussed.

Exponential utility maximization under model uncertainty for unbounded endowments