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An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories

Harin, Alexander (2015): An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories.

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Abstract

An existence theorem is proved for the case of a discrete random variable with finite support. If the random variable takes on values in a finite interval and there is a lower non-zero bound on its dispersion, then non-zero bounds (or non-zero “forbidden zones”) on its expectation exist near the borders of the interval. The theorem can be used in utility and prospect theories, in particular, in the analysis of Prelec’s probability weighting function.

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