We study single period asset allocation problems of the investor who maximizes the expected utility with respect to non-additive beliefs. The non-additive beliefs of the investor model the presence of an uncertainty and they are assumed to be consistent with the Maxmin expected utility theory of Gilboa and Schmeidler (1989). The proportional transaction costs are incorporated into the model. We provide the explicit form solutions for the bounds of no-transaction regions which completely determine the optimal policy of the investor
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