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A family of premium principles based on mixtures of TVaRs

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  • Sordo, Miguel A.
  • Castaño-Martínez, Antonia
  • Pigueiras, Gema

Abstract

Risk-adjusted distributions are commonly used in actuarial science to define premium principles. In this paper, we claim that an appropriate risk-adjusted distribution, besides satisfying other desirable properties, should be well-behaved under conditioning with respect to the original risk distribution. Based on a sequence of such risk-adjusted distributions, we introduce a family of premium principles that gradually incorporate the degree of risk-aversion of the insurer in the risk loading. Members of this family are particular distortion premium principles that can be represented as mixtures of TVaRs, where the weights in the mixture reflect the attitude toward risk of the insurer. We make a systematic study of this family of premium principles.

Suggested Citation

  • Sordo, Miguel A. & Castaño-Martínez, Antonia & Pigueiras, Gema, 2016. "A family of premium principles based on mixtures of TVaRs," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 397-405.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:397-405
    DOI: 10.1016/j.insmatheco.2016.07.006
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    References listed on IDEAS

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    7. van Heerwaarden, A. E. & Kaas, R., 1992. "The Dutch premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 11(2), pages 129-133, August.
    8. Gerber, Hans U., 1981. "The Esscher Premium Principle: A Criticism. Comment," ASTIN Bulletin, Cambridge University Press, vol. 12(2), pages 139-140, December.
    9. Bühlmann, H. & Gagliardi, B. & Gerber, H. U. & Straub, E., 1977. "Some Inequalities for Stop-Loss Premiums," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 75-83, January.
    10. Yang, Jianping & Zhuang, Weiwei & Hu, Taizhong, 2014. "Lp-metric under the location-independent risk ordering of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 321-324.
    11. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
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    Cited by:

    1. Wei Wang & Huifu Xu, 2023. "Preference robust distortion risk measure and its application," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 389-434, April.
    2. Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    3. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    4. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    5. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    6. Psarrakos, Georgios & Vliora, Polyxeni, 2021. "Sensitivity analysis and tail variability for the Wang’s actuarial index," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 147-152.
    7. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    8. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.
    9. 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.
    10. Sánchez-Sánchez, M. & Sordo, M.A. & Suárez-Llorens, A. & Gómez-Déniz, E., 2019. "Deriving Robust Bayesian Premiums Under Bands Of Prior Distributions With Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 147-168, January.
    11. Jorge Navarro & Camilla Calì & Maria Longobardi & Fabrizio Durante, 2022. "Distortion representations of multivariate distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 925-954, October.

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    More about this item

    Keywords

    Tail value-at-risk; Premium principle; Risk measure; Order statistics; Distortion function;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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