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

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.