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New methods in the classical economics of uncertainty: comparing risks

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  • Christian Gollier

    (Toulouse School of Economics)

  • Miles S. Kimball

    (University of Colorado Boulder)

Abstract

Second-order stochastic dominance answers the question “Under what conditions will all risk-averse agents prefer $$\tilde{x}_2$$ x ~ 2 to $$\tilde{x}_1$$ x ~ 1 ?” Consider the following related question: “Under what conditions will all risk-averse agents who prefer lottery $$\tilde{x}_1$$ x ~ 1 to a reference lottery $$\tilde{\omega }$$ ω ~ also prefer lottery $$\tilde{x}_2$$ x ~ 2 to that reference lottery?” Each of these two questions is an example of a broad category of questions of great relevance for the economics of risk. The second question is an example of a contingent risk comparison, while the question behind second-order stochastic dominance is an example of a non-contingent risk comparison. The stochastic order arising from a contingent risk comparison is obviously weaker than that arising from the corresponding non-contingent risk comparison, but we show that the two stochastic orders are closely related, so that the answer to a non-contingent risk comparison problem always provides the answer to the corresponding contingent risk comparison problem. In addition to showing the connection between parallel contingent and non-contingent risk comparison problems, we articulate a method for solving both kinds of problems using the “basis” approach. The basis approach has often been used implicitly, but we argue that there is value in making its use explicit, particularly in indicating which new, previously unsolved problems can readily be solved by the basis approach and which cannot.

Suggested Citation

  • Christian Gollier & Miles S. Kimball, 2018. "New methods in the classical economics of uncertainty: comparing risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
  • Handle: RePEc:pal:genrir:v:43:y:2018:i:1:d:10.1057_s10713-018-0026-y
    DOI: 10.1057/s10713-018-0026-y
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    Cited by:

    1. Cary Deck & Sebastian Ebert & Andreas Richter, 2018. "Special issue in honor of Harris Schlesinger: New developments in the study of risk preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 1-4, May.
    2. Light, Bar & Perlroth, Andres, 2021. "The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. Christian Gollier & Miles S. Kimball, 2018. "Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 397-430, June.
    4. Jordi Caballe & Joan Esteban, 2007. "Stochastic Dominance and Absolute Risk Aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 89-110, January.
    5. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
    6. Jouini, Elyès & Marin, Jean-Michel & Napp, Clotilde, 2010. "Discounting and divergence of opinion," Journal of Economic Theory, Elsevier, vol. 145(2), pages 830-859, March.
    7. Burton Hollifield & Alan Kraus, 2009. "Defining Bad News: Changes in Return Distributions That Decrease Risky Asset Demand," Management Science, INFORMS, vol. 55(7), pages 1227-1236, July.
    8. Gollier, Christian, 1996. "Deductible insurance and production: A comment," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 55-59, December.
    9. Octave Jokung & Sovan Mitra, 2019. "Asset Prices and Changes in Risk within a Bivariate Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(1), pages 47-60, March.

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    More about this item

    Keywords

    Stochastic dominance; Central riskiness; Comparative statics under uncertainty; Increase in risk;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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