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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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  • 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
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    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.
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    10. 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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    3. Chichilnisky, Graciela, 2017. "The Topology of Change: Foundations of Probability with Black Swans," MPRA Paper 86080, University Library of Munich, Germany.
    4. Chanel, Olivier & Chichilnisky, Graciela, 2013. "Valuing life: Experimental evidence using sensitivity to rare events," Ecological Economics, Elsevier, vol. 85(C), pages 198-205.
    5. Luc Lauwers, 2016. "Intergenerational Equity, Efficiency, and Constructibility," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 191-206, Springer.
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    8. Chollete, Lorán, 2009. "The Propagation of Financial Extremes," Discussion Papers 2008/25, Norwegian School of Economics, Department of Business and Management Science.
    9. Marcello Basili & Antonio Nicita, 2020. "The Covid-19/SARS CoV-2 pandemic outbreak and the risk of institutional failures," Department of Economics University of Siena 823, Department of Economics, University of Siena.
    10. Chollete, Loran & Jaffee, Dwight, 2009. "Economic Implications of Extreme and Rare Events," UiS Working Papers in Economics and Finance 2009/32, University of Stavanger.
    11. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    12. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    13. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 184-192, March.
    14. Julien Blasco & Graciela Chichilnisky, 2015. "Risk Aversion and Catastrophic Risks: the Pill Experiment," Papers 1604.05672, arXiv.org.
    15. Chichilnisky, Graciela, 2011. "Catastrophic Risks with Finite or Infinite States," MPRA Paper 88760, University Library of Munich, Germany.
    16. 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.
    17. 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.
    18. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-25.
    19. Ouandlous, Arav & Barkoulas, John T. & Pantos, Themis D., 2022. "Extremity in bitcoin market activity," The Journal of Economic Asymmetries, Elsevier, vol. 26(C).
    20. Andrea Rampa, 2020. "Climate change, catastrophes and Dismal Theorem: a critical review [Klimawandel, Katastrophen und das „Dismal Theorem“: eine kritische Überprüfung]," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 40(2), pages 113-136, October.
    21. Buchholz, Wolfgang & Schymura, Michael, 2012. "Expected utility theory and the tyranny of catastrophic risks," Ecological Economics, Elsevier, vol. 77(C), pages 234-239.
    22. 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.
    23. 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.

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