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From sure to strong diversification

Author

Listed:
  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Ghizlane Lakhnati

Abstract

This paper presents a characterization of weak risk aversion in terms of preference for sure diversification. Similarly, we show that strong risk aversion can be characterized by weakening preference for diversification,as introduced by Dekel (Econometrica 57:163,1989), in what we call preference for strong diversification.

Suggested Citation

  • Alain Chateauneuf & Ghizlane Lakhnati, 2007. "From sure to strong diversification," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00271265, HAL.
    • Handle: RePEc:hal:cesptp:hal-00271265
    DOI: 10.1007/s00199-006-0126-2
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    References listed on IDEAS

    as
    1. Hong Chew Soo & Hui Mao Mei, 1995. "A Schur Concave Characterization of Risk Aversion for Non-expected Utility Preferences," Journal of Economic Theory, Elsevier, vol. 67(2), pages 402-435, December.
    2. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    3. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    4. Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
    5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    6. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
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    8. Abouda, Moez & Chateauneuf, Alain, 2002. "Characterization of symmetrical monotone risk aversion in the RDEU model," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 1-15, September.
    9. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
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    11. Allais Maurice, 1990. "CARDINAL UTILITY: History, Empirical Findings, and Applications An Overview," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 1(2), pages 3-40, June.
    12. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    13. Moez Abouda & Alain Chateauneuf, 2002. "Positivity of bid-ask spreads and symmetrical monotone risk aversion ," Theory and Decision, Springer, vol. 52(2), pages 149-170, March.
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    Cited by:

    1. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    2. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2014. "Optimal Risk Sharing with Optimistic and Pessimistic Decision Makers," Working Papers 2014-579, Department of Research, Ipag Business School.
    3. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2017. "Optimal sharing with an infinite number of commodities in the presence of optimistic and pessimistic agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 131-157, January.
    4. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Diversification preferences in the theory of choice," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 143-174, November.
    5. Ola Mahmoud, 2022. "The Willingness to Pay for Diversification," Management Science, INFORMS, vol. 68(8), pages 6235-6249, August.
    6. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    7. Moez Abouda, 2008. "Decreasing absolute risk aversion: some clarification," Post-Print halshs-00270648, HAL.
    8. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    9. Gilles Boevi Koumou, 2016. "Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit," Papers 1608.05024, arXiv.org, revised Aug 2016.
    10. Moez Abouda & Elyess Farhoud, 2010. "Anti-comonotone random variables and anti-monotone risk aversion," Post-Print halshs-00497444, HAL.
    11. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    12. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Naive Diversification Preferences and their Representation," Papers 1611.01285, arXiv.org, revised Nov 2016.
    13. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    14. Jean Baccelli, 2018. "Risk Attitudes in Axiomatic Decision Theory: a Conceptual Perspective," Post-Print hal-01620886, HAL.
    15. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    16. Moez Abouda & Elyess Farhoud, 2010. "Risk aversion and Relationships in model-free," Post-Print halshs-00492170, HAL.

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    More about this item

    Keywords

    Weak risk aversion; Strong risk aversion; Diversification;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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