Choquet rank-dependent utility with an exogenous unambiguous source

We axiomatize the Choquet rank-dependent utility model within a Savage framework with an exogenous source of pure risk. This model is a decision model under ambiguity, serving as a conceptual generalization of the Choquet expected utility model. The model unifies risk and ambiguity and reduces to the rank-dependent utility for pure risks. Our axiomatization uses two main axioms for biseparable preferences, along with some regularity axioms. A benefit of this axiomatization is that the fairly weak regularity axioms guarantee the existence of matching probabilities. Further, we discuss ambiguity attitudes for the CRDU model. We characterize these attitudes by properties of the associated matching probabilities and show that the supermodularity of the matching probability provides a robust representation. Finally, we show that under an additional Property, this model has a different representation using act-dependent distortion functions.