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What attitudes to risk underlie distortion risk measure choices?

Author

Listed:
  • Jaume Belles-Sampera

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Montserrat Guillén

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Miguel Santolino

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

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 discrete Choquet integrals provide informa- tion 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

  • Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2015. "What attitudes to risk underlie distortion risk measure choices?," Working Papers 2015-05, Universitat de Barcelona, UB Riskcenter.
    • Handle: RePEc:bak:wpaper:201505
    as

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    File URL: http://www.ub.edu/rfa/research/WP/UBriskcenterWP201505.pdf
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    References listed on IDEAS

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    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
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    4. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
    5. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    6. Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
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    Cited by:

    1. Dominik Krężołek, 2016. "The Gluevar Risk Measure And Investor’S Attitudes To Risk– An Application To The Non-Ferrous Metals Market," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 305-316, June.
    2. Mercedes Ayuso & Montserrat Guillen & Jens Perch Nielsen, 2019. "Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data," Transportation, Springer, vol. 46(3), pages 735-752, June.
    3. Manuela Alcañiz & Aïda Solé-Auró, 2018. "Ageing and health-related quality of life: evidence from Catalonia (Spain)," Working Papers 2018-01, Universitat de Barcelona, UB Riskcenter.
    4. Dominik Krężołek, 2016. "The Gluevar Risk Measure And Investor’s Attitudes To Risk–An Application To The Non-Ferrous Metals Market," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 305-316, June.

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    Keywords

    Risk management; Risk tolerance; GlueVaR; Solvency II; Basel III.;
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