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The Logic of Partial-Risk Aversion: Paradox Lost

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  • Pratt, John W

Abstract

One rational individual may be willing to pay less than another to insure a risk "epsilon" when another risk w is present even though he would pay more to insure any isolated risk, and even though E(" epsilon" w) = 0 for all w. Noticing this, Ross (1981) proposed excluding such reversals and gave equivalent analytical conditions. Reconsidering, we explain why some reversals are natural and show that prohibiting them has peculiar and undesirable properties. Although we also simplify the conditions and prove them necessary for partial-risk portfolio results, we conclude that they represent revealing restrictions on comparative statics rather than natural implications of increased aversion to risk. Copyright 1990 by Kluwer Academic Publishers

Suggested Citation

  • Pratt, John W, 1990. "The Logic of Partial-Risk Aversion: Paradox Lost," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 105-113, June.
    • Handle: RePEc:kap:jrisku:v:3:y:1990:i:2:p:105-13
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    Cited by:

    1. 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.
    2. W. Henry Chiu, 2005. "Skewness Preference, Risk Aversion, and the Precedence Relations on Stochastic Changes," Management Science, INFORMS, vol. 51(12), pages 1816-1828, December.
    3. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    4. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    5. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    6. Keenan, Donald C. & Snow, Arthur, 2012. "Ross risk vulnerability for introductions and changes in background risk," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 197-206.
    7. 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.
    8. Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Risk aversion with two risks: A theoretical extension," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 100-105.
    9. 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.
    10. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    11. Finkelshtain, Israel & Kella, Offer & Scarsini, Marco, 1999. "On risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 239-250, March.
    12. Donald C., Rudow, 2005. "Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance," MPRA Paper 41191, University Library of Munich, Germany, revised 07 Jun 2005.
    13. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    14. Christoph Heinzel, 2016. "Precautionary Saving in the Large: nth-Degree Deteriorations in Return Risk," FOODSECURE Working papers 42, LEI Wageningen UR.
    15. Louis R. Eeckhoudt & Roger J. A. Laeven, 2021. "Probability Premium and Attitude Towards Probability," Papers 2105.00054, arXiv.org.
    16. Christoph Heinzel, 2016. "Precautionary Saving in the Large under Higher-Order Risk and Recursive Utility," FOODSECURE Working papers 43, LEI Wageningen UR.
    17. 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.

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