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The topology of fear

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  • Chichilnisky, Graciela

Abstract

For many years experimental observations have raised questions about the rationality of economic agents--for example, the Allais Paradox or the Equity Premium Puzzle. The problem is a narrow notion of rationality that disregards fear. This article extends the notion of rationality with new axioms of choice under uncertainty and the decision criteria they imply (Chichilnisky, G., 1996a. An axiomatic approach to sustainable development. Social Choice andWelfare 13, 257-321; Chichilnisky, G., 2000. An axiomatic approach to choice under uncertainty with Catastrophic risks. Resource and Energy Economics; Chichilnisky, G., 2002. Catastrophical Risk. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd., Chicester). In the absence of catastrophes, the old and the new approach coincide, and both lead to standard expected utility. A sharp difference emerges when facing rare events with important consequences, or catastrophes. Theorem 1 establishes that a classic axiom of choice under uncertainty - Arrow's Monotone Continuity axiom, or its relatives introduced by DeGroot, Villegas, Hernstein and Milnor - postulate rational behavior that is [`]insensitive' to rare events as defined in (Chichilnisky, G., 1996a. An axiomatic approach to sustainable development. Social Choice andWelfare 13, 257-321; Chichilnisky, G., 2000. An axiomatic approach to choice under uncertainty with Catastrophic risks. Resource and Energy Economics; Chichilnisky, G., 2002. Catastrophical Risk. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd., Chicester). Theorem 2 replaces this axiom with another that allows extreme responses to extreme events, and characterizes the implied decision criteria as a combination of expected utility with extremal responses. Theorems 1 and 2 offer a new understanding of rationality consistent with previously unexplained observations about decisions involving rare and catastrophic events, decisions involving fear, the Equity Premium Puzzle, [`]jump diffusion' processes and [`]heavy tails', and it agrees with (Debreu, G., 1953. Valuation equilibrium and Pareto optimum. Proceedings of the National Academy of Sciences, 40, 588-592) formulation of market behavior and his proof of Adam Smith's Invisible Hand theorem.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 12 (December)
Pages: 807-816

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Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:807-816

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Decision theory Risk Uncertainty Catastrophes Fear Topology Axioms of decision theory Representation theory Rare events Equity premium puzzle Allais paradox Experimental work Functional MRIs Rare events Catastrophes;

References

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  1. Rajnish Mehra, 2003. "The Equity Premium: Why is it a Puzzle?," NBER Working Papers 9512, National Bureau of Economic Research, Inc.
  2. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, Econometric Society, vol. 49(2), pages 359-68, March.
  3. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 24(3), pages 401-421, November.
  4. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer, Springer, vol. 14(2), pages 303-318.
  5. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  6. Chichilnisky, Graciela, 1996. "Financial Innovation in Property Catastrophe Reinsurance: The Convergence of Insurance and Capital Markets," MPRA Paper 8333, University Library of Munich, Germany.
  7. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, Econometric Society, vol. 63(6), pages 1255-80, November.
  8. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer, Springer, vol. 13(2), pages 231-257, April.
  9. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 15(2), pages 145-161, March.
  10. Chichilnisky, G., 1992. "The Cone Condition Properness, and Extremely Desirable Commodities," Discussion Papers, Columbia University, Department of Economics 1992_09, Columbia University, Department of Economics.
  11. Graciela Chichilnisky & Olga Gorbachev, 2004. "Volatility in the knowledge economy," Discussion Papers, Columbia University, Department of Economics 0304-13, Columbia University, Department of Economics.
  12. McFadden, Daniel, 1975. "An example of the non-existence of Malinvaud prices in a tight economy," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 2(1), pages 17-19, March.
  13. Graciela Chichilnisky & Ho-Mou Wu, 2006. "General equilibrium with endogenous uncertainty and default," Discussion Papers, Columbia University, Department of Economics 0506-29, Columbia University, Department of Economics.
  14. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
  15. Chichilnisky, Graciela, 2000. "An axiomatic approach to choice under uncertainty with catastrophic risks," Resource and Energy Economics, Elsevier, Elsevier, vol. 22(3), pages 221-231, July.
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Cited by:
  1. S. Scrieciu & Valerie Belton & Zaid Chalabi & Reinhard Mechler & Daniel Puig, 2014. "Advancing methodological thinking and practice for development-compatible climate policy planning," Mitigation and Adaptation Strategies for Global Change, Springer, Springer, vol. 19(3), pages 261-288, March.
  2. Graciela Chichilnisky, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Working Papers, LAMETA, Universtiy of Montpellier 09-07, LAMETA, Universtiy of Montpellier, revised Aug 2009.
  3. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, Elsevier, vol. 59(2), pages 184-192, March.
  4. Chollete, Lorán, 2008. "The Propagation of Financial Extremes: An Application to Subprime Market Spillovers," Discussion Papers, Department of Business and Management Science, Norwegian School of Economics 2008/2, Department of Business and Management Science, Norwegian School of Economics.
  5. Robert Kast, 2011. "Managing financial risks due to natural catastrophes," Working Papers, HAL hal-00610241, HAL.
  6. Olivier Chanel & Graciela Chichilnisky, 2009. "The influence of fear in decisions: Experimental evidence," Journal of Risk and Uncertainty, Springer, Springer, vol. 39(3), pages 271-298, December.
  7. Chollete, Lorán, 2009. "The Propagation of Financial Extremes," Discussion Papers, Department of Business and Management Science, Norwegian School of Economics 2008/25, Department of Business and Management Science, Norwegian School of Economics.
  8. Chanel, Olivier & Chichilnisky, Graciela, 2013. "Valuing life: Experimental evidence using sensitivity to rare events," Ecological Economics, Elsevier, Elsevier, vol. 85(C), pages 198-205.
  9. Luc LAUWERS, 2010. "Intergenerational equity, efficiency and constructability," Center for Economic Studies - Discussion papers, Katholieke Universiteit Leuven, Centrum voor Economische Studiën ces10.22, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  10. Chollete, Loran & Jaffee, Dwight, 2009. "Economic Implications of Extreme and Rare Events," UiS Working Papers in Economics and Finance, University of Stavanger 2009/32, University of Stavanger.

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