Lower Previsions for Unbounded Random Variables
In order to generalise Walley’s theory of lower previsions, which are real-valued maps on bounded random variables, to arbitrary random variables, we introduce extended lower previsions as extended real-valued maps on arbitrary, not necessarily bounded, random variables. We suggest and motivate conditions for avoiding sure loss, coherence and linearity, we construct a natural extension, and we suggest a way to generalise some of the more advanced topological results from the existing theory of lower previsions.
KeywordsLinear Space Rational Agent Natural Extension Linear Prevision Lower Prevision
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