Abstract
Depending on the school of thought, expected utility theory states that choices among lotteries either should be made or actually made by maximizing the expected value of a real valued function of the outcomes—a utility function. This article provides a look at some of the functional analytic results used in expected utility theory. I concentrate on applications to the theory of stochastic dominance relations and the revealed preference approach to expected utility. Few of these results are deep, given the underlying tools, but many of them are not widely known, and their combination is novel. In particular, the revealed preference results of Border [4] are extended to higher degree stochastic dominance relations.
I thank Mike Maxwell for pointing out errors in an early draft of this paper.
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Border, K.C. (1991). Functional Analytic Tools for Expected Utility Theory. In: Positive Operators, Riesz Spaces, and Economics. Studies in Economic Theory, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58199-1_4
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DOI: https://doi.org/10.1007/978-3-642-58199-1_4
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