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Normalized measures of concavity and Ross’s strongly more risk averse order

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  • Liqun Liu
  • Jack Meyer

Abstract

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981 ) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitudes towards risk…”. Ross does not provide a corresponding measure of risk aversion. This paper uses a normalized measure of concavity to characterize the Ross definition of strongly more risk averse on bounded intervals. Other properties and uses of these normalized measures of concavity are also presented. Copyright Springer Science+Business Media New York 2013

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  • 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.
    • Handle: RePEc:kap:jrisku:v:47:y:2013:i:2:p:185-198
    DOI: 10.1007/s11166-013-9173-9
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    Cited by:

    1. Liqun Liu & Jack Meyer, 2017. "The Increasing Convex Order and the Trade–off of Size for Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 881-897, September.
    2. AJ A. Bostian & Christoph Heinzel, 2018. "Comparative precautionary saving under higher-order risk and recursive utility," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 95-114, May.
    3. 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.
    4. Li, Jingyuan & Liu, Liqun, 2014. "The monetary utility premium and interpersonal comparisons," Economics Letters, Elsevier, vol. 125(2), pages 257-260.
    5. 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.
    6. Brandtner, Mario & Kürsten, Wolfgang, 2014. "Decision making with Conditional Value-at-Risk and spectral risk measures: The problem of comparative risk aversion," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100615, Verein für Socialpolitik / German Economic Association.
    7. Brandtner, Mario & Kürsten, Wolfgang, 2015. "Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 268-280.
    8. AJ A. Bostian & Christoph Heinzel, 2018. "Comparative precautionary saving under higher-order risk and recursive utility," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 95-114, May.

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    More about this item

    Keywords

    Normalized concavity measures; Arrow-Pratt risk aversion; Strongly more risk averse; D81;
    All these keywords.

    JEL classification:

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

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