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’s axiomatic theory of choice under uncertainty, and within new extensions of the theory that are speci…cally 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 de…ned 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) allowes extreme responses to extreme events, and requires equal treatement of rare and frequent events, deriving the new decision criterion the axioms imply. These are expected utility combined with purely …nitely addditive 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 Groot’s axioms in the foundation of statistics and Debreu’s 1953 work on Adam Smith’s Invisible The results of this article were presented at Greqam Universite de Marseille, December 18th 2008, at LAMETA Universite de Montpellier, December 19th and 20th 2008, at the NBER-NSF General Equilibrium Conference in Honor of Gerard Debreu, October 6 2006, at the Statistics Department of Columbia University October 11 2006, at the Fields Institute for Mathematical Research Conference on Catastrohpic Risks, 1996, Toronto Canada, and at a Sta¤ Seminar of NHH, University of Oslo Norway March 21 2007. 1 UNEDITED VERSION. The final version is to appear in the International Journal of Green Economics, 2009