Risk averse decision making under catastrophic risk

A nonstandard probabilistic setting for modeling of the risk of catastrophic events is presented. It allows random variables to take on infinitely large negative values with non-zero probability, which corresponds to catastrophic consequences unmeasurable in monetary terms, e.g. loss of human lives. Thanks to this extension, the safety-first principle is proved to be consistent with traditional axioms of rational behavior, such as monotonicity, continuity, and risk aversion. Also, a robust preference relation is introduced, and an example of a monotone robust preference relation, sensitive to catastrophic events in the sense of Chichilnisky [14], is provided. The suggested setting is demonstrated in evaluating nuclear power plant projects when the probability of a catastrophe is itself a random variable.