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New methods in the classical economics of uncertainty: comparing risks

Author

Listed:
  • Christian Gollier

    () (Toulouse School of Economics)

  • Miles S. Kimball

    (University of Colorado Boulder)

Abstract

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 Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
  • Handle: RePEc:kap:geneva:v:43:y:2018:i:1:d:10.1057_s10713-018-0026-y
    DOI: 10.1057/s10713-018-0026-y
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    References listed on IDEAS

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    1. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    2. R. G. Vickson, 1975. "Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables," Management Science, INFORMS, vol. 21(12), pages 1438-1446, August.
    3. Meyer, Jack & Ormiston, Michael B, 1985. "Strong Increases in Risk and Their Comparative Statics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 425-437, June.
    4. 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.
    5. Vickson, R. G., 1975. "Stochastic Dominance for Decreasing Absolute Risk Aversion," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(05), pages 799-811, December.
    6. Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, vol. 14(2), pages 326-336, April.
    7. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    8. Jouini, E. & Napp, C., 2008. "On Abel's concept of doubt and pessimism," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3682-3694, November.
    9. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    10. Kraus, Marvin, 1979. "A comparative statics theorem for choice under risk," Journal of Economic Theory, Elsevier, vol. 21(3), pages 510-517, December.
    11. repec:dau:papers:123456789/2326 is not listed on IDEAS
    12. Christian Gollier, 1997. "A Note on Portfolio Dominance," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 147-150.
    13. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1329-1344.
    14. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
    15. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    16. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 73-85.
    17. 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.
    18. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    19. Dionne, Georges & Eeckhoudt, Louis & Gollier, Christian, 1993. "Increases in Risk and Linear Payoffs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 309-319, May.
    20. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
    21. Meyer, Jack & Ormiston, Michael B., 1983. "The comparative statics of cumulative distribution function changes for the class of risk averse agents," Journal of Economic Theory, Elsevier, vol. 31(1), pages 153-169, October.
    22. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
    23. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    24. 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.
    25. Arthur Hau, 2008. "When Is a Coinsurance-Type Insurance Policy Inferior or Even Giffen?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 343-364.
    26. Cherbonnier, Frédéric & Gollier, Christian, 2015. "Decreasing aversion under ambiguity," Journal of Economic Theory, Elsevier, vol. 157(C), pages 606-623.
    27. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    28. Eeckhoudt, Louis & Hansen, Pierre, 1980. "Minimum and Maximum Prices, Uncertainty, and the Theory of the Competitive Firm," American Economic Review, American Economic Association, vol. 70(5), pages 1064-1068, December.
    29. Black, Jane M & Bulkley, I George, 1989. "A Ratio Criterion for Signing the Effects of an Increase in Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(1), pages 119-130, February.
    30. Jewitt, Ian, 1986. "A note on comparative statics and stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 249-254, June.
    31. Michael Landsberger & Isaac Meilijson, 1993. "Mean-preserving Portfolio Dominance," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 479-485.
    32. Erin Baker, 2009. "Optimal Policy under Uncertainty and Learning about Climate Change: A Stochastic Dominance Approach," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(5), pages 721-747, October.
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    Cited by:

    1. 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.
    2. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
    3. 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.
    4. 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.
    5. Gollier, Christian, 1996. "Deductible insurance and production: A comment," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 55-59, December.

    More about this item

    Keywords

    Stochastic dominance; Central riskiness; Comparative statics under uncertainty; Increase in risk;

    JEL classification:

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

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