Choices Under Risk and Uncertainty with Windfall Gains and Catastrophic Losses

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet integral is formalized when the decision-maker holds both capacities and probabilities. A characterization of the decision-maker's behaviour is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones.