Stable Non-standard Imprecise Probabilities

Abstract

Abstract. Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered "practically impossible" but not "logically impossible".

Strict Coherence on Many-Valued Events

“…Finally, further work will also tell us whether the characterisation of strict coherence for many-valued events provided in this paper has an interesting counterpart when probabilities are extended to the hyperreals along the lines of [19,28]. As implied by [28,Theorem 4.2] this setting is immune to the limitations arising from the potential lack, in general, of faithful states of MV-algebras.…”