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Catastrophical Risk

Extremes and Environmental Risk

  1. Graciela Chichilnisky

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vac008

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Chichilnisky, G. 2006. Catastrophical Risk. Encyclopedia of Environmetrics. 1.

Author Information

  1. Columbia University, NY, USA

Publication History

  1. Published Online: 15 SEP 2006


This article analyses decision under uncertainty, motivated by problems emerging from global environmental risks. These are typically low-probability events with major irreversible consequences. For such risks the Von Neumann–Morgenstern (NM) Axioms for decision-making under uncertainty are not appropriate, since they are insensitive to low-probability events. The article introduces an alternative set of axioms that require sensitivity to both low and large probability events. Through a representation theorem in functional analysis, the results characterize all the operators whose maximization leads to the fulfillment of these axioms. They involve a convex combination of expected utility and a criterion based on the desire to avoid low-probability and potentially catastrophical events. It is shown that the new axioms help resolve the Allais paradox. Open questions about risk aversion, games under uncertainty and calculus of variations are discussed.


  • risk;
  • catastrophes;
  • uncertainty;
  • financial management;
  • risk management;
  • mathematical methods;
  • financial theory;
  • insurance;
  • financial risk management