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New Results for Additive and Multiplicative Risk Apportionment

Author

Listed:
  • Henri Loubergé

    () (UNIGE - Université de Genève)

  • Yannick Malevergne

    () (PRISM-Sorbonne - PRISM - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Panthéon-Sorbonne)

  • Béatrice Rey

    (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

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 halshs-02100855, HAL.
  • Handle: RePEc:hal:wpaper:halshs-02100855
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02100855
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    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. 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.
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    7. 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.
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    More about this item

    Keywords

    Preserved preference ranking; Multiplicative risks; Constant relative risk aversion; Additive risks; Risk apportionment;

    JEL classification:

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

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