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The topology of fear

  • Chichilnisky, Graciela

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
  2. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  3. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, vol. 49(2), pages 359-68, March.
  4. McFadden, Daniel, 1975. "An example of the non-existence of Malinvaud prices in a tight economy," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 17-19, March.
  5. Graciela Chichilnisky & Olga Gorbachev, 2004. "Volatility in the knowledge economy," Economic Theory, Springer, vol. 24(3), pages 531-547, October.
  6. Chichilnisky, Graciela & Wu, Ho-Mou, 2006. "General equilibrium with endogenous uncertainty and default," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 499-524, August.
  7. Chichilnisky, Graciela, 1993. "The Cone Condition, Properness, and Extremely Desirable Commodities," Economic Theory, Springer, vol. 3(1), pages 177-82, January.
  8. Rajnish Mehra, 2003. "The Equity Premium: Why is it a Puzzle?," NBER Working Papers 9512, National Bureau of Economic Research, Inc.
  9. Chichilnisky, Graciela, 1996. "Financial Innovation in Property Catastrophe Reinsurance: The Convergence of Insurance and Capital Markets," MPRA Paper 8333, University Library of Munich, Germany.
  10. Chichilnisky, Graciela, 1995. "An axiomatic approach to sustainable development," MPRA Paper 8609, University Library of Munich, Germany.
  11. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
  12. 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.
  13. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  14. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
  15. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer, vol. 14(2), pages 303-318.
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