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Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

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2.2Von NeumannMorgenstern representation

Suppose that each possible choice for our economic agent corresponds to a probability distribution on a given set of scenarios. Thus, the set X can be identified with a subset M of the set M1(S,S) of all probability distributions on a measurable space (S,S). In the context of the theory of choice, the elements of M are sometimes called lotteries. We will assume in the sequel that M is convex. The aim of this section is to characterize those preference orders on M which allow for a numerical representation U of the form

where u is a real function on S.

Definition 2.17. A numerical representation U of a ...

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