The paper investigates a decision-making process involving both risk and ambiguity. Differently from existing papers [Basili, M., Chateauneuf, A., Fontini, F., 2005. Choices under ambiguity with familiar and unfamiliar outcomes, Theory and Decision 58,195-207; Chichilnisky, G., 2000. Axiomatic approach to choice under uncertainty with catastrophic risks. Resources and Energy Economics 22, 221-231; Chichilnisky, G., 2002. In: El-Shaarawi, A.,H., Piegorsch, W.W. (Eds.), Catastropic Risks. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd, Chichester, UK, pp. 274-279], we assume that, in a Choquet Expected Utility framework, the decision-maker is pessimistic with respect to unfamiliar (catastrophic) losses, optimistic with respect...