Stable non-standard imprecise probabilities

Stability arises as the consistency criterion in a betting inter- pretation 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 ex- tends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered “practically impossible” but not “logically impossible”.