This paper concerns the well known paradox of inconsistency of the maximum-expected-utility (MEU) and the maximum-expected-log (MEL) criteria in investment dynamic models for large horizons. The goal of the paper is to consider this phenomenon at the level of premises, and to suggest a generalized criterion, namely the rank dependent expected utility (RDEU) approach which allows to ``bridge the gap'' between the MEU and MEL criteria. The preference order in the RDEU approach is preserved by the functional
U (F ) = ∫0∞u (x )d Ѱ (F (x )),
where F is a probability distribution, u is a utility function, and Ѱ is a transforming or weighting function: the subject ``transforms'' the real distribution function F (x ) into another one, Ѱ (F (x )), assigning different weights to different probabilities. One of main goals of the paper is to establish conditions on the tail of Ѱ , and on the utility function u, under which the asymptotically optimal investment in the long run corresponds to the MEL policy. The result of the paper is relevant also to the questions of the survival of economic agents in the market and the accuracy of their predictions or beliefs.
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