Conditional Lower Previsions for Unbounded Random Quantities

In this paper, a theory of conditional coherent lower previsions for arbitrary random quantities, including unbounded ones, is introduced, based on Williams's notion of coherence, and extending at the same time unconditional theories studied for unbounded random quantities known from the literature. We generalize a well-known envelope theorem to the domain of all contingent random quantities. Finally, using this duality result, we prove equivalence between maximal and Bayes actions in decision making for convex option sets