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Diversification, convex preferences and non-empty core in the Choquet expected utility model

Author

Listed:
  • Jean-Marc Tallon

    () (EUREQua, CNRS-Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'Hôpital,75647 Paris Cedex 13, FRANCE)

  • Alain Chateauneuf

    () (CERMSEM, Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'Hôpital,75647 Paris Cedex 13, FRANCE)

Abstract

We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely "sure diversification." We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:19:y:2002:i:3:p:509-523
    Note: Received: July 27, 1999; revised version: November 7, 2000
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    Cited by:

    1. 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.
    2. repec:hal:journl:halshs-00348822 is not listed on IDEAS
    3. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    4. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    5. Chateauneuf, A. & Grabisch, M. & Rico, A., 2008. "Modeling attitudes toward uncertainty through the use of the Sugeno integral," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1084-1099, December.
    6. repec:hal:journl:halshs-00341174 is not listed on IDEAS
    7. Chateauneuf, Alain & Ventura, Caroline, 2010. "The no-trade interval of Dow and Werlang: Some clarifications," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 1-14, January.
    8. Gilles Boevi Koumou, 2016. "Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit," Papers 1608.05024, arXiv.org, revised Aug 2016.
    9. Galand, Lucie & Perny, Patrice & Spanjaard, Olivier, 2010. "Choquet-based optimisation in multiobjective shortest path and spanning tree problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 303-315, July.
    10. repec:hal:journl:halshs-00429573 is not listed on IDEAS
    11. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    12. repec:hal:journl:halshs-00442861 is not listed on IDEAS
    13. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    14. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Naive Diversification Preferences and their Representation," Papers 1611.01285, arXiv.org, revised Nov 2016.
    15. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-25, July.
    16. Guerdjikova, Ani, 2004. "Preference for diversification with similarity considerations," Papers 04-48, Sonderforschungsbreich 504.
    17. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    18. repec:hal:journl:halshs-00327700 is not listed on IDEAS
    19. Wakker, Peter P., 2005. "Decision-foundations for properties of nonadditive measures: general state spaces or general outcome spaces," Games and Economic Behavior, Elsevier, vol. 50(1), pages 107-125, January.
    20. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.

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