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On the properties of high-order non-monetary measures for risks

Author

Listed:
  • Christophe Courbage

    (University of Applied Sciences Western Swizterland (HES-SO))

  • Henri Loubergé

    (University of Geneva)

  • Béatrice Rey

    (GATE UMR 5824, Univ Lyon, Université Lumière Lyon 2)

Abstract

This paper investigates how welfare losses for facing high-order risk increases change when the risk environment of the decision maker is altered. To that aim, we define the nth-order utility premium as a measure of pain associated with facing the passage of one risk to a more severe one and we examine some of its properties. Changes in risk are expressed through the concept of stochastic dominance of order n. The paper investigates more particularly welfare changes of merging increases in risk, first ignoring background risks, then taking them into account. Merging increases in risk may be beneficial or not, depending on whether background risks are considered and how. The paper also provides conditions on individual preferences for superadditivity of the nth-order utility premium. The results confirm the importance and usefulness of two analytical concepts: mixed risk aversion and risk apportionment.

Suggested Citation

  • Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    • Handle: RePEc:pal:genrir:v:43:y:2018:i:1:d:10.1057_s10713-018-0029-8
    DOI: 10.1057/s10713-018-0029-8
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    Cited by:

    1. Cary Deck & Sebastian Ebert & Andreas Richter, 2018. "Special issue in honor of Harris Schlesinger: New developments in the study of risk preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 1-4, May.
    2. Loubergé, Henri & Malevergne, Yannick & Rey, Béatrice, 2020. "New Results for additive and multiplicative risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 140-151.
    3. Christophe Courbage & Béatrice Rey, 2020. "On temperance and risk spreading," Theory and Decision, Springer, vol. 88(4), pages 527-539, May.
    4. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    5. Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    6. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.

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    More about this item

    Keywords

    Mixed risk aversion; Risk apportionment; Merging increases in risk; Superadditivity; nth-order utility premium;
    All these keywords.

    JEL classification:

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

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