Catastrophic Risks

Catastrophic risks are rare events with major consequences, e.g. catastrophic climate change or extinction of a species. The article summarizes decision theory involving catastrophic risks within Von Neumann is axiomatic theory of choice under uncertainty, and within new extensions of the theory that are specifically designed for rare events of major consequences. The classic expected utility theory is insensitive to rare events no matter how catastrophic. Its insensitivity emerges from the requirement of nearby responses to nearby stimuli, where 'nearby' is defined in terms of averages. Thus Arrow's Monotone Continuity Axiom and its relatives in Hernstein and Milnor anticipate average responses to extreme events. This leads to 'expected utility' that is insensitive to extreme risks. In a new axiomatic extension the author (Chichilnisky 1996, 2000, 2002) allows extreme responses to extreme events, and requires equal treatment of rare and frequent events, deriving the new decision criterion the axioms imply. These are expected utility combined with purely finitely additive measures that focus on catastrophes, and reproduce 'fat tails' distributions. Continuity is based on the 'topology of fear' introduced in Chichilnisky (2009), and is linked to De Grootís axioms in the foundation of statistics and Debreu is 1953 work on Adam Smith is Invisible Hand. The balance between the classic and the new axioms tests the limits of non- parametric estimation in Hilbert spaces, Chichilnisky (2008). Recent work by Le Doux, Chichilnisky and Chanel provide experimental evidence on choices that invoke fear.