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Evolutionary credibility risk premium

Author

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  • Chen, Yongzhao
  • Cheung, Ka Chun
  • Choi, Hugo Ming Cheung
  • Yam, Sheung Chi Phillip

Abstract

This article provides the first systematic study on the risk premium calibration under the celebrated evolutionary credibility models which had been studied in Jones and Gerber (1975) and Albrecht (1985) but only for net premium, while our work now simultaneously estimates the process variance and the hypothetical mean. Our objective is to minimize the mean square deviation of the empirical estimates from the respective theoretical mean and process variance, which leads to extending the set of classical normal equations. Despite that no more closed-form solutions of the normal equations can be obtained, we obtain an effective numerical scheme featuring a novel recursive LU algorithm for the progressively enlarging coefficient matrices, and we shall also demonstrate its effectiveness through several common time series models, namely ARMA. Our proposed method can also be viewed as a robust extension of the recent SURE estimator used in statistics literature, which assumes the underlying data being i.i.d. with the Normal-Inverse-Wishart structure, while we allow a temporal dependence structure among the data without specifying the probability model.

Suggested Citation

  • Chen, Yongzhao & Cheung, Ka Chun & Choi, Hugo Ming Cheung & Yam, Sheung Chi Phillip, 2020. "Evolutionary credibility risk premium," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 216-229.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:216-229
    DOI: 10.1016/j.insmatheco.2020.04.015
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    References listed on IDEAS

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    1. Pitselis, Georgios, 2017. "Risk measures in a quantile regression credibility framework with Fama/French data applications," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 122-134.
    2. Kim, Joseph H.T. & Jeon, Yongho, 2013. "Credibility theory based on trimming," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 36-47.
    3. Schinzinger, Edo & Denuit, Michel & Christiansen, Marcus, 2016. "A multivariate evolutionary credibility model for mortality improvement rates," LIDAM Reprints ISBA 2016019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    5. Xacur, Oscar Alberto Quijano & Garrido, José, 2018. "Bayesian credibility for GLMs," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 180-189.
    6. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    7. Sundt, Bjorn, 1982. "Invariantly recursive credibility estimation," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 219-240, July.
    8. Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.
    9. Albrecht, Peter, 1985. "An Evolutionary Credibility Model for Claim Numbers," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 1-17, April.
    10. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, December.
    11. Schinzinger, Edo & Denuit, Michel M. & Christiansen, Marcus C., 2016. "A multivariate evolutionary credibility model for mortality improvement rates," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 70-81.
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    Cited by:

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    More about this item

    Keywords

    Credibility theory; Bühlmann’s evolutionary model; Variance (shrinkage) estimator; Risk-loaded premium; LU factorization; ARMA;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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