[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/gat/wpaper/1915.html
   My bibliography  Save this paper

New Results for Additive and Multiplicative Risk Apportionment

Author

Listed:
  • Henri Loubergé

    (Geneva School of Economics and Management, University of Geneva, Uni Mail, Pont d'Arve 40, 1211 Geneva 4)

  • Yannick Malevergne

    (Université Paris 1 Panthéon Sorbonne, PRISM Sorbonne EA 4101 and LabEx ReFi, F-75005 Paris, France)

  • Béatrice Rey

    (Univ Lyon, Université Lumière Lyon 2, GATE UMR 5824, F-69130 Ecully, France)

Abstract
We start by pointing out a simple property of risk apportionment with additive risks in the general stochastic dominance context defined by Eeckhoudt et al. (2009b). Quite generally, an observed preference for risk apportionment with additive risks in a specific risk environment is preserved when the decision-maker is confronted to other risk situations, so long as the total order of stochastic dominance relationships among pairs of risks remains the same. Our objective is to check whether this simple property also holds for multiplicative risk environments. We show that this is not the case, in general, but that the property holds and more strongly for the case of CRRA utility functions. This is due to a particular feature of CRRA functions that we unveil.

Suggested Citation

  • Henri Loubergé & Yannick Malevergne & Béatrice Rey, 2019. "New Results for Additive and Multiplicative Risk Apportionment," Working Papers 1915, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    • Handle: RePEc:gat:wpaper:1915
    as

    Download full text from publisher

    File URL: ftp://ftp.gate.cnrs.fr/RePEc/2019/1915.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. EECKHOUDT, Louis, 2012. "Beyond risk aversion: why, how and what's next?," LIDAM Reprints CORE 2514, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Cary Deck & Harris Schlesinger, 2010. "Exploring Higher Order Risk Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1403-1420.
    3. Attema, Arthur E. & l’Haridon, Olivier & van de Kuilen, Gijs, 2019. "Measuring multivariate risk preferences in the health domain," Journal of Health Economics, Elsevier, vol. 64(C), pages 15-24.
    4. Michel Denuit & Béatrice Rey, 2013. "Another look at risk apportionment," Post-Print halshs-03353453, HAL.
    5. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    6. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    7. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    8. Y Malevergne & B Rey, 2010. "Preserving preference rankings under non-financial background risk," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1302-1308, August.
    9. 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.
    10. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    11. Jean, William H, 1980. "The Geometric Mean and Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 151-158, March.
    12. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    13. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    14. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    15. Cary Deck & Harris Schlesinger, 2018. "On The Robustness Of Higher Order Risk Preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 313-333, June.
    16. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 875-886, November.
    17. Eeckhoudt, Louis & Etner, Johanna & Schroyen, Fred, 2009. "The values of relative risk aversion and prudence: A context-free interpretation," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 1-7, July.
    18. Wang, Jianli & Li, Jingyuan, 2010. "Multiplicative risk apportionment," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 79-81, July.
    19. Louis Eeckhoudt, 2012. "Beyond Risk Aversion: Why, How and What's Next?*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 141-155, September.
    20. Trautmann, Stefan T. & Kuilen, Gijs van de, 2018. "Higher order risk attitudes: A review of experimental evidence," European Economic Review, Elsevier, vol. 103(C), pages 108-124.
    21. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    22. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    23. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    24. 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.
    25. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    26. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    27. Gollier, Christian, 2019. "Variance stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 1-8.
    28. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    29. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    30. Hongxia Wang, 2019. "Generalized Multiplicative Risk Apportionment," Risks, MDPI, vol. 7(2), pages 1-9, June.
    31. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    32. Denuit, Michel & Rey, Beatrice, 2013. "Another look at risk apportionment," LIDAM Reprints ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    33. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    34. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    35. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    36. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
    37. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    38. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    39. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    40. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    2. Ignacia Benitez & Claudio A. Bonilla & Marcos Vergara, 2024. "Hybrid entrepreneurship and risk," Small Business Economics, Springer, vol. 63(3), pages 1171-1196, October.

    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. 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.
    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. Ignacia Benitez & Claudio A. Bonilla & Marcos Vergara, 2024. "Hybrid entrepreneurship and risk," Small Business Economics, Springer, vol. 63(3), pages 1171-1196, October.
    5. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    6. Hongxia Wang, 2019. "Generalized Multiplicative Risk Apportionment," Risks, MDPI, vol. 7(2), pages 1-9, June.
    7. Sebastian Ebert & Diego C. Nocetti & Harris Schlesinger, 2018. "Greater Mutual Aggravation," Management Science, INFORMS, vol. 64(6), pages 2809-2811, June.
    8. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    9. 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.
    10. Takao Asano & Yusuke Osaki, 2022. "Precautionary Saving against Correlation under Risk and Ambiguity," KIER Working Papers 1071, Kyoto University, Institute of Economic Research.
    11. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2013. "Economic consequences of Nth-degree risk increases and Nth-degree risk attitudes," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 199-224, October.
    12. 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.
    13. Sebastian Ebert & Daniel Wiesen, 2014. "Joint measurement of risk aversion, prudence, and temperance," Journal of Risk and Uncertainty, Springer, vol. 48(3), pages 231-252, June.
    14. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    15. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    16. Nocetti, Diego & Smith, William T., 2015. "Changes in risk and strategic interaction," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 37-46.
    17. Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.
    18. Colasante, Annarita & Riccetti, Luca, 2020. "Risk aversion, prudence and temperance: It is a matter of gap between moments," Journal of Behavioral and Experimental Finance, Elsevier, vol. 25(C).
    19. Denuit, Michel & Rey, Beatrice, 2012. "Uni- And Multidimensional Risk Attitudes: Some Unifying Theorems," LIDAM Discussion Papers ISBA 2012014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Trautmann, Stefan T. & Kuilen, Gijs van de, 2018. "Higher order risk attitudes: A review of experimental evidence," European Economic Review, Elsevier, vol. 103(C), pages 108-124.

    More about this item

    Keywords

    Additive risks; Constant relative risk aversion; Multiplicative risks; Preserved preference ranking; Risk apportionment;
    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:gat:wpaper:1915. 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: Nelly Wirth (email available below). General contact details of provider: https://edirc.repec.org/data/gateefr.html .

    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.