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Catastrophic Risks with Finite or Infinite States

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  • Chichilnisky, Graciela

Abstract

Catastrophic risks are rare events with major consequences, such as market crashes, catastrophic climate change, asteroids or the extinction of a species. We show that classic expected utility theory based on Von Neumann axioms is insensitive to rare events no matter how catastrophic. Its insensitivity emerges from a requirement of continuity (e.g. Arrow's Monotone Continuity Axiom, and its relatives as defined by De Groot, Hernstein and Milnor) that anticipate average responses to extreme events. This leads to countably additive measures and `expected utility' that are insensitive to extreme risks. In a new axiomatic extension, the author (Chichilnisky 1996, 2000, 2002) 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 explain the presistent observations of distributions with "fat tails" in earth sciences and financial markets. Continuity is based on the `topology of fear' introduced in Chichilnisky (2009), and is linked to Debreu's 1953 work on Adam Smith's Invisible Hand. The balance between the classic and the new axioms tests the limits of non- parametric estimation in Hilbert spaces, Chichilnisky (2008).. extending the foundations of probability & statistics (Chichilnisky 2009 and 2010) to include "black swans" or rare events, and finite as well as infinite state spaces.

Suggested Citation

  • Chichilnisky, Graciela, 2011. "Catastrophic Risks with Finite or Infinite States," MPRA Paper 88760, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:88760
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    References listed on IDEAS

    as
    1. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 184-192, March.
    2. Chichilnisky, Graciela, 2000. "An axiomatic approach to choice under uncertainty with catastrophic risks," Resource and Energy Economics, Elsevier, vol. 22(3), pages 221-231, July.
    3. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
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    5. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    6. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    7. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    8. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    9. Rajnish Mehra, 2003. "The Equity Premium: Why is it a Puzzle?," NBER Working Papers 9512, National Bureau of Economic Research, Inc.
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    More about this item

    Keywords

    catastrophic risks; choice under uncertainty; black swans; green economics; incompleteness of mathematics; axiom of choice;
    All these keywords.

    JEL classification:

    • Q0 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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