A rational decision rule with extreme events

Risks induced by extreme events are characterized by small or ambiguous probabilities, catastrophic losses, or windfall gains. Through a new functional, that mimics the restricted Bayes–Hurwicz criterion within the Choquet expected utility approach, it is possible to represent the decision-maker behavior facing both risky (large and reliable probability) and extreme (small or ambiguous probability) events. A new formalization of the precautionary principle is shown and a new functional, which encompasses both extreme outcomes and expectation of all the possible results for every act, is claimed.