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Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories

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  • Quiggin, John
  • Chambers, Robert G

Abstract

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave. Copyright 1998 by Kluwer Academic Publishers

Suggested Citation

  • Quiggin, John & Chambers, Robert G, 1998. "Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 121-137, November.
    • Handle: RePEc:kap:jrisku:v:17:y:1998:i:2:p:121-37
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    Citations

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    Cited by:

    1. Raphaël Giraud, 2012. "Money matters: an axiomatic theory of the endowment effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 303-339, June.
    2. John Quiggin & Robert Chambers, 2007. "Supermodularity and the Comparative Statics of Risk," Theory and Decision, Springer, vol. 62(2), pages 97-117, March.
    3. John Quiggin & Robert G. Chambers, 2006. "The state-contingent approach to production under uncertainty ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 50(2), pages 153-169, June.
    4. Robert G. Chambers & John Quiggin, 2007. "Dual Approaches to the Analysis of Risk Aversion," Economica, London School of Economics and Political Science, vol. 74(294), pages 189-213, May.
    5. Robert G. Chambers & Tigran Melkonyan & John Quiggin, 2022. "Incomplete preferences, willingness to pay, and willingness to accept," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 727-761, October.
    6. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    7. Chambers, Robert G. & Quiggin, John, 2005. "Linear-risk-tolerant, invariant risk preferences," Economics Letters, Elsevier, vol. 86(3), pages 303-309, March.
    8. Chambers, Robert G. & Quiggin, John, 2003. "Indirect certainty equivalents for the firm facing price and production uncertainty," Economics Letters, Elsevier, vol. 78(3), pages 309-316, March.
    9. John Quiggin, 2022. "Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory," Theory and Decision, Springer, vol. 92(3), pages 717-729, April.
    10. Juan Sebastián Lleras & Evan Piermont & Richard Svoboda, 2019. "Asymmetric gain–loss reference dependence and attitudes toward uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 669-699, October.
    11. Cho, Bo-Hyun & Hooker, Neal H., 2004. "The Opportunity Cost Of Food Safety Regulation - An Output Directional Distance Function Approach," Working Papers 28316, Ohio State University, Department of Agricultural, Environmental and Development Economics.
    12. Cho, Bo-Hyun & Hooker, Neal H., 2004. "Measuring The Impact Of Food Safety Regulation-An Output Directional Distance Function Approach," 2004 Annual meeting, August 1-4, Denver, CO 20016, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Chambers, Robert G. & Quiggin, John, 1999. "Production Insurance and Input Use: An Analytical Framework," Working Papers 197859, University of Maryland, Department of Agricultural and Resource Economics.
    14. Grant, Simon & Kajii, Atsushi, 2007. "The epsilon-Gini-contamination multiple priors model admits a linear-mean-standard-deviation utility representation," Economics Letters, Elsevier, vol. 95(1), pages 39-47, April.
    15. Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
    16. Quiggin, John & Chambers, Robert G., 2006. "Supermodularity and risk aversion," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 1-14, July.
    17. Jaenicke, Edward C. & Larson, James A., 2001. "Production Risk Revisited In A Stochastic Frontier Framework: Evaluating Noise And Inefficiency In Cover Crop Systems," 2001 Annual meeting, August 5-8, Chicago, IL 20477, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    18. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    19. Quiggin, John & Chambers, R.G.Robert G., 2004. "Invariant risk attitudes," Journal of Economic Theory, Elsevier, vol. 117(1), pages 96-118, July.

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