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What attitudes to risk underlie distortion risk measure choices?

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  • Belles-Sampera, Jaume
  • Guillen, Montserrat
  • Santolino, Miguel

Abstract

Understanding the attitude to risk implicit within a risk measure sheds some light on the way in which decision makers perceive losses. In this paper, a two-stage strategy is developed to characterize the underlying risk attitude involved in a risk evaluation, when executed by the family of distortion risk measures. First, we show that aggregation indicators defined for Choquet integrals provide information about the implicit global risk attitude of the agent. Second, an analysis of the distortion function offers a local description of the agent’s stance on risk in relation to the occurrence of accumulated losses. Here, the concepts of absolute risk attitude and local risk attitude arise naturally. An example is provided to illustrate the usefulness of this strategy for characterizing risk attitudes in an insurance company.

Suggested Citation

  • Belles-Sampera, Jaume & Guillen, Montserrat & Santolino, Miguel, 2016. "What attitudes to risk underlie distortion risk measure choices?," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 101-109.
    • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:101-109
    DOI: 10.1016/j.insmatheco.2016.02.005
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    References listed on IDEAS

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    Cited by:

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    2. Jilber Urbina & Miguel Santolino & Montserrat Guillen, 2021. "Covariance Principle for Capital Allocation: A Time-Varying Approach," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    3. Krężołek Dominik & Trzpiot Grażyna, 2020. "Risk Management on the Metals Market," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 24(2), pages 86-97, June.
    4. Hou, Yanxi & Wang, Xing, 2019. "Nonparametric inference for distortion risk measures on tail regions," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 92-110.
    5. Cai, Jun & Wang, Ying & Mao, Tiantian, 2017. "Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 105-116.
    6. 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.
    7. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.

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    More about this item

    Keywords

    Risk management; Tolerance; Risk behavior; GlueVaR; Degree of orness;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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