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Exponential utility maximization under model uncertainty for unbounded endowments. (English) Zbl 1419.91285
Summary: 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.

91B16 Utility theory
49L20 Dynamic programming in optimal control and differential games
60G42 Martingales with discrete parameter
91G80 Financial applications of other theories
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