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

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2.5Robust preferences on asset profiles

In this section, we discuss the structure of preferences for assets on a more fundamental level. Instead of assuming that the distributions of assets are known and that preferences are defined on a set of probability measures, we will take as our basic objects the assets themselves. An asset will be viewed as a function which associates real-valued payoffs to possible scenarios. More precisely, X will denote a set of bounded measurable functions X on some measurable set (Ω,F). We emphasize that no a priori probability measure is given on (Ω,F). In other words, we are facing uncertainty instead of risk.

We assume that X is endowed with a preference relation . In view of the financial interpretation, it is ...

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