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ON ADMISSIBLE STRATEGIES IN ROBUST UTILITY MAXIMIZATION (Revised in March 2012, Forthcoming in "Mathematics and Financial Economics")

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Abstract

The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a “good definition” of admissible strategies to obtain an optimizer. Under certain assumptions, especially a time-consistency property of the set P of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of those whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with one of P ∈ P.
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