Keywords: catastrophic risks, risk, uncertainty, outliers, rare events, axioms of choice, topology, fear, green economics, extreme events, mathematical economics, statistics
Catastrophic risks are rare events with major consequences and of great interest to green economics. The article investigates the way economics deals with catastrophic risks. Classic expected utility theory is insensitive to rare events no matter how important these may be, based on the axioms of Von Neumann (1944), Arrow (1971) and DeGroot (1970/2004) that define proximity of observations in terms of 'averages' obliterating outliers. A new axiomatic extension to the theory of choice introduced new axioms that are sensitive to rare events, and characterised the criteria that these imply (Chichilnisky, 1996, 2000, 2002, 2010; Lawuers, 1993). These are expected utility combined with a new term that focuses on extremal events, explaining 'fat tails' and 'outliers'. Continuity based on 'the topology of fear' provides the required sensitivity to rare events (Chichilnisky, 2009c). Experimental evidence for the new axiomatic treatment is in Chanel and Chichilnisky (2009). The results relate to Debreu's (1954) work on Adam Smith's Invisible Hand and Le Doux's (1996) work on the neurological responses to fear.