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Admissible Sets of Utility Functions in Expected Utility Maximization
William R. Russell
Tae Kun Seo
Abstract
A generalization of the St. Petersburg paradox has led Menger to observe that utility functions must be bounded to insure existence of expected utility when probability distributions are unrestricted. It is clear that the admissible set of utility functions can be expanded as restrictions are imposed on the distribution functions under consideration. This paper provides a schema for determining the admissible utility functions for each probability distribution set defined by a minimum order requirement on the moments of the distribution.
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