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Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models

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  • Michèle D. Cohen

    (C.E.M.E., Université de Paris I, 12 Place du Panthéon, 75005 Paris, France)

Abstract

The non-expected-utility theories of decision under risk have favored the appearance of new notions of increasing risk like monotone increasing risk (based on the notion of comonotonic random variables) or new notions of risk aversion like aversion to monotone increasing risk, in better agreement with these new theories. After a survey of all the possible notions of increasing risk and of risk aversion and their intrinsic definitions, we show that contrary to expected-utility theory where all the notions of risk aversion have the same characterization ( u concave), in the framework of rank-dependent expected utility (one of the most well known of the non-expectedutility models), the characterizations of all these notions of risk aversion are different. Moreover, we show that, even in the expected-utility framework, the new notion of monotone increasing risk can give better answers to some problems of comparative statics such as in portfolio choice or in partial insurance. This new notion also can suggest more intuitive approaches to inequalities measurement. The Geneva Papers on Risk and Insurance Theory (1995) 20, 73–91. doi:10.1007/BF01098959

Suggested Citation

  • Michèle D. Cohen, 1995. "Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 73-91, June.
    • Handle: RePEc:pal:genrir:v:20:y:1995:i:1:p:73-91
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    Cited by:

    1. Hindriks, Jean & De Donder, Philippe, 2003. "The politics of redistributive social insurance," Journal of Public Economics, Elsevier, vol. 87(12), pages 2639-2660, December.
    2. Jan Werner, 2009. "Risk and risk aversion when states of nature matter," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 231-246, November.
    3. Langlais, Eric, 2006. "Criminals and risk attitude," MPRA Paper 1149, University Library of Munich, Germany, revised 15 Sep 2006.
    4. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    5. Éric Langlais, 2010. "Les criminels aiment-ils le risque ?," Revue économique, Presses de Sciences-Po, vol. 61(2), pages 263-280.
    6. Louis R. Eeckhoudt & Roger J. A. Laeven, 2021. "Probability Premium and Attitude Towards Probability," Papers 2105.00054, arXiv.org.
    7. Armantier, Olivier & Treich, Nicolas, 2009. "Star-shaped probability weighting functions and overbidding in first-price auctions," Economics Letters, Elsevier, vol. 104(2), pages 83-85, August.
    8. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    9. Jammernegg, Werner & Kischka, Peter, 2013. "Risk preferences of a newsvendor with service and loss constraints," International Journal of Production Economics, Elsevier, vol. 143(2), pages 410-415.
    10. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    11. Yotam Gafni & Moshe Tennenholtz, 2022. "Optimal Mechanism Design for Agents with DSL Strategies: The Case of Sybil Attacks in Combinatorial Auctions," Papers 2210.15181, arXiv.org, revised Jul 2023.
    12. Eeckhoudt, Louis, 2001. "Espérance d’utilité et nouveaux modèles de choix dans le risque : une connivence cachée," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(4), pages 499-516, décembre.
    13. Deutscher, Christian & Gürtler, Marc & Gürtler, Oliver & DeVaro, Jed, 2020. "Firm choice and career success - theory and evidence," European Economic Review, Elsevier, vol. 127(C).
    14. Giuseppe, DE FEO & Jean, HINDRIKS, 2005. "Efficiency of Competition in Insurance Markets with Adverse Selection," Discussion Papers (ECON - Département des Sciences Economiques) 2005042, Université catholique de Louvain, Département des Sciences Economiques.
    15. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    16. Roger, Patrick, 2000. "Properties of bid and ask reservation prices in the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 269-285, November.
    17. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.
    18. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    19. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.

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