IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-01471888.html
   My bibliography  Save this paper

On the properties of non-monetary measures for risks

Author

Listed:
  • Christophe Courbage

    (Geneva School of Business Administration)

  • Henri Loubergé

    (UNIGE - Université de Genève = University of Geneva)

  • Béatrice Rey

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper investigates how welfare losses for facing risks change as the risk environment of the decision-maker is altered. To that aim, we define the risk apportionment of order n (RAn) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one. Changes in risks are expressed through the concept of stochastic dominance of order n. Three configurations of risk exposures are considered. The paper first shows how the RAn utility premium is modified when initial wealth becomes riskier. Second, the paper provides conditions on individual preferences for superadditivity of the RAn utility premium. Third, the paper investigates welfare changes of merging increases in risks. These results offer new interpretations of the sign of higher derivatives of the utility function.

Suggested Citation

  • Christophe Courbage & Henri Loubergé & Béatrice Rey, 2017. "On the properties of non-monetary measures for risks," Working Papers halshs-01471888, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01471888
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01471888
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01471888/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Eeckhoudt, Louis & Schlesinger, Harris, 2009. "On the utility premium of Friedman and Savage," Economics Letters, Elsevier, vol. 105(1), pages 46-48, October.
    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. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    5. 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.
    6. Eeckhoudt, L. & Gollier, C., 1998. "Which Shape for the Cost Curve of Risk?," Papers 98.490, Toulouse - GREMAQ.
    7. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    8. 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.
    9. Eeckhoudt, L. & Bauwens, L. & Briys, E. & Scarmure, P., 1990. "The Law Of Large (Small?) Numbers And The Demand For Insurance," G.R.E.Q.A.M. 90a03, Universite Aix-Marseille III.
    10. Georges Dionne (ed.), 2013. "Handbook of Insurance," Springer Books, Springer, edition 2, number 978-1-4614-0155-1, September.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    2. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    3. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    4. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    5. Michel Denuit & Liqun Liu, 2014. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," Theory and Decision, Springer, vol. 76(2), pages 287-295, February.
    6. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    7. 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.
    8. Sebastian Ebert & Diego C. Nocetti & Harris Schlesinger, 2018. "Greater Mutual Aggravation," Management Science, INFORMS, vol. 64(6), pages 2809-2811, June.
    9. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    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. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    12. Denuit, Michel & Liu, Liqun, 2013. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," LIDAM Discussion Papers ISBA 2013007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Christoph Heinzel & Richard Peter, 2021. "Precautionary motives with multiple instruments [Motifs de précaution en cas de multiples instruments]," Working Papers hal-03484875, HAL.
    14. Heinzel, Christoph & Peter, Richard, 2021. "Precautionary motives with multiple instruments," Working Papers 316521, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    15. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    16. Li, Jingyuan & Liu, Liqun, 2014. "The monetary utility premium and interpersonal comparisons," Economics Letters, Elsevier, vol. 125(2), pages 257-260.
    17. 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.
    18. Sebastian Ebert, 2013. "Moment characterization of higher-order risk preferences," Theory and Decision, Springer, vol. 74(2), pages 267-284, February.
    19. 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.
    20. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.

    More about this item

    Keywords

    risk apportionment; superadditivity; RA-n utility premium;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-01471888. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.