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Infinite Previsions and Finitely Additive Expectations

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journal contribution
posted on 01.01.2014, 00:00 authored by Mark J. Schervish, Teddy Seidenfeld, Joseph B. Kadane

We give an extension of de Finetti’s concept of coherence to unbounded (but real-valued) random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of the Fundamental Theorem of Prevision to deal with conditional previsions and unbounded random variables.