IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v45y2009i12p807-816.html
   My bibliography  Save this article

The topology of fear

Author

Listed:
  • 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.

Suggested Citation

  • Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:807-816
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(09)00063-9
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, vol. 49(2), pages 359-368, March.
    3. Chichilnisky, Graciela, 1996. "Financial Innovation in Property Catastrophe Reinsurance: The Convergence of Insurance and Capital Markets," MPRA Paper 8333, University Library of Munich, Germany.
    4. 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.
    5. Chichilnisky, Graciela, 1993. "The Cone Condition, Properness, and Extremely Desirable Commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 177-182, January.
    6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    7. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 303-318.
    8. 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.
    9. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    10. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    11. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    12. Rajnish Mehra, 2003. "The Equity Premium: Why is it a Puzzle?," NBER Working Papers 9512, National Bureau of Economic Research, Inc.
    13. 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.
    14. 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.
    15. Graciela Chichilnisky & Olga Gorbachev, 2004. "Volatility in the knowledge economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 531-547, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, vol. 19(3), pages 261-288, March.
    2. DeCanio, Stephen J. & Fremstad, Anders, 2013. "Game theory and climate diplomacy," Ecological Economics, Elsevier, vol. 85(C), pages 177-187.
    3. Chanel, Olivier & Chichilnisky, Graciela, 2013. "Valuing life: Experimental evidence using sensitivity to rare events," Ecological Economics, Elsevier, vol. 85(C), pages 198-205.
    4. Luc Lauwers, 2012. "Intergenerational equity, efficiency, and constructibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 227-242, February.
    5. Luterbacher Urs & Sandi Carmen, 2014. "Breaking the Dynamics of Emotions and Fear in Conflict and Reconstruction," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 20(3), pages 1-44, August.
    6. Robert Kast, 2011. "Managing financial risks due to natural catastrophes," Working Papers hal-00610241, HAL.
    7. Chollete, Lorán, 2009. "The Propagation of Financial Extremes," Discussion Papers 2008/25, Norwegian School of Economics, Department of Business and Management Science.
    8. Chollete, Loran & Jaffee, Dwight, 2009. "Economic Implications of Extreme and Rare Events," UiS Working Papers in Economics and Finance 2009/32, University of Stavanger.
    9. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    10. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    11. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 184-192, March.
    12. Julien Blasco & Graciela Chichilnisky, 2015. "Risk Aversion and Catastrophic Risks: the Pill Experiment," Papers 1604.05672, arXiv.org.
    13. Olivier Chanel & Graciela Chichilnisky, 2009. "The influence of fear in decisions: Experimental evidence," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 271-298, December.
    14. Hayato Nakanishi, 2017. "Quasi-experimental evidence for the importance of accounting for fear when evaluating catastrophic events," Empirical Economics, Springer, vol. 52(2), pages 869-894, March.
    15. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-25.
    16. Buchholz, Wolfgang & Schymura, Michael, 2012. "Expected utility theory and the tyranny of catastrophic risks," Ecological Economics, Elsevier, vol. 77(C), pages 234-239.
    17. Norman Schofield, 2015. "Climate Change, Collapse and Social Choice Theory," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 007-035, October.
    18. Chollete, Lorán, 2008. "The Propagation of Financial Extremes: An Application to Subprime Market Spillovers," Discussion Papers 2008/2, Norwegian School of Economics, Department of Business and Management Science.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:807-816. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.