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On the properties of high-order non-monetary measures for risks

Author

Listed:
  • Christophe Courbage

    (University of Applied Sciences Western Swizterland (HES-SO))

  • Henri Loubergé

    (University of Geneva)

  • Béatrice Rey

    (GATE UMR 5824, Univ Lyon, Université Lumière Lyon 2)

Abstract

This paper investigates how welfare losses for facing high-order risk increases change when the risk environment of the decision maker is altered. To that aim, we define the nth-order utility premium as a measure of pain associated with facing the passage of one risk to a more severe one and we examine some of its properties. Changes in risk are expressed through the concept of stochastic dominance of order n. The paper investigates more particularly welfare changes of merging increases in risk, first ignoring background risks, then taking them into account. Merging increases in risk may be beneficial or not, depending on whether background risks are considered and how. The paper also provides conditions on individual preferences for superadditivity of the nth-order utility premium. The results confirm the importance and usefulness of two analytical concepts: mixed risk aversion and risk apportionment.

Suggested Citation

  • Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    • Handle: RePEc:pal:genrir:v:43:y:2018:i:1:d:10.1057_s10713-018-0029-8
    DOI: 10.1057/s10713-018-0029-8
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    1. Cary Deck & Harris Schlesinger, 2010. "Exploring Higher Order Risk Effects," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1403-1420.
    2. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    3. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    4. Jean, William H, 1980. "The Geometric Mean and Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 151-158, March.
    5. Eeckhoudt, L. & Gollier, C., 1998. "Which Shape for the Cost Curve of Risk?," Papers 98.490, Toulouse - GREMAQ.
    6. Menegatti, Mario, 2011. "The risk premium and the effects of risk on agents utility," Research in Economics, Elsevier, vol. 65(2), pages 89-94, June.
    7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    8. Eeckhoudt, Louis & Schlesinger, Harris, 2009. "On the utility premium of Friedman and Savage," Economics Letters, Elsevier, vol. 105(1), pages 46-48, October.
    9. Christophe Courbage & Béatrice Rey, 2010. "On Non‐Monetary Measures In The Face Of Risks And The Signs Of The Derivatives," Bulletin of Economic Research, Wiley Blackwell, vol. 62(3), pages 295-304, July.
    10. 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.
    11. Sebastian Ebert, 2013. "Moment characterization of higher-order risk preferences," Theory and Decision, Springer, vol. 74(2), pages 267-284, February.
    12. Christophe Courbage & Béatrice Rey, 2010. "On Non-Monetary Measures In The Face Of Risks And The Signs Of The Derivatives," Post-Print halshs-03353474, HAL.
    13. Li, Jingyuan & Liu, Liqun, 2014. "The monetary utility premium and interpersonal comparisons," Economics Letters, Elsevier, vol. 125(2), pages 257-260.
    14. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    15. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    16. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82(5), pages 1913-1943, September.
    17. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    18. Patrick Roger, 2011. "Mixed risk aversion and preference for risk disaggregation: a story of moments," Theory and Decision, Springer, vol. 70(1), pages 27-44, January.
    19. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
    20. Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    21. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    22. Patrick L. Brockett & Linda L. Golden, 1987. "A Class of Utility Functions Containing all the Common Utility Functions," Management Science, INFORMS, vol. 33(8), pages 955-964, August.
    23. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    24. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    25. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    26. Georges Dionne (ed.), 2013. "Handbook of Insurance," Springer Books, Springer, edition 2, number 978-1-4614-0155-1, June.
    27. 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.
    28. Jean, William H, 1984. "The Harmonic Mean and Other Necessary Conditions for Stochastic Dominance," Journal of Finance, American Finance Association, vol. 39(2), pages 527-534, June.
    29. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
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    Cited by:

    1. Loubergé, Henri & Malevergne, Yannick & Rey, Béatrice, 2020. "New Results for additive and multiplicative risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 140-151.
    2. Cary Deck & Sebastian Ebert & Andreas Richter, 2018. "Special issue in honor of Harris Schlesinger: New developments in the study of risk preferences," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 1-4, May.
    3. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    4. Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    5. Christophe Courbage & Béatrice Rey, 2020. "On temperance and risk spreading," Theory and Decision, Springer, vol. 88(4), pages 527-539, May.
    6. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.

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    More about this item

    Keywords

    Mixed risk aversion; Risk apportionment; Merging increases in risk; Superadditivity; nth-order utility premium;
    All these keywords.

    JEL classification:

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

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