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Substituting one risk increase for another: A method for measuring risk aversion

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  • Liu, Liqun
  • Meyer, Jack

Abstract

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an mth degree risk increase, where n>m⩾1. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.

Suggested Citation

  • Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:6:p:2706-2718
    DOI: 10.1016/j.jet.2013.10.002
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. repec:spr:joecth:v:64:y:2017:i:1:d:10.1007_s00199-016-0978-z is not listed on IDEAS
    2. Wang, Jianli & Li, Jingyuan, 2014. "Decreasing Ross risk aversion: Higher-order generalizations and implications," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 136-142.
    3. Huang, James & Stapleton, Richard, 2015. "The utility premium of Friedman and Savage, comparative risk aversion, and comparative prudence," Economics Letters, Elsevier, vol. 134(C), pages 34-36.
    4. Li, Jingyuan & Liu, Liqun, 2014. "The monetary utility premium and interpersonal comparisons," Economics Letters, Elsevier, vol. 125(2), pages 257-260.
    5. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2014. "Decreasing downside risk aversion and background risk," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 59-63.
    6. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2017. "Health and portfolio choices: A diffidence approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 273-279.
    7. repec:eee:ecolet:v:159:y:2017:i:c:p:116-118 is not listed on IDEAS
    8. Louis Eeckhoudt & Liqun Liu & Jack Meyer, 2017. "Restricted increases in risk aversion and their application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 161-181, June.
    9. Pierre Chaigneau & Louis Eeckhoudt, 2015. "Downside Risk Neutral Probabilities," Cahiers de recherche 1521, CIRPEE.
    10. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    11. Liu, Liqun, 2014. "Precautionary saving in the large: nth degree deteriorations in future income," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 169-172.
    12. repec:eee:mateco:v:71:y:2017:i:c:p:119-128 is not listed on IDEAS
    13. Denuit, Michel & Liu, Liqun & Meyer, Jack, 2014. "A separation theorem for the weak s-convex orders," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 279-284.
    14. Liqun Liu & Jack Meyer, 2013. "Normalized measures of concavity and Ross’s strongly more risk averse order," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 185-198, October.
    15. Eeckhoudt, Louis R. & Laeven, Roger J.A., 2015. "The probability premium: A graphical representation," Economics Letters, Elsevier, vol. 136(C), pages 39-41.
    16. repec:kap:geneva:v:43:y:2018:i:1:d:10.1057_s10713-018-0030-2 is not listed on IDEAS
    17. Louis R. Eeckhoudt & Roger J. A. Laeven, 2015. "Risk Aversion in the Small and in the Large under Rank-Dependent Utility," Papers 1512.08037, arXiv.org.

    More about this item

    Keywords

    Risk premium; Rate of substitution; Risk aversion; Comparative risk aversion; Expected utility model;

    JEL classification:

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

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