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Tweedie multivariate semi-parametric credibility with the exchangeable correlation

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  • Jeong, Himchan

Abstract

This article proposes a framework for determining credibility premiums for multiple coverages in a compound risk model with Tweedie distribution. The framework builds upon previous results on credibility premium and provides an explicit multivariate credibility premium formula that is applicable to the Tweedie family assuming that the unobserved heterogeneity for the multiple coverage have the common correlation. The practical applicability of the proposed framework is evaluated through simulation and empirical analysis using the LGPIF dataset, which includes claims and policy characteristics data for various types of coverages observed over time. The findings suggest that the proposed framework can be useful in ratemaking practice by incorporating a non-trivial dependence structure among the multiple types of claims.

Suggested Citation

  • Jeong, Himchan, 2024. "Tweedie multivariate semi-parametric credibility with the exchangeable correlation," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 13-21.
    • Handle: RePEc:eee:insuma:v:115:y:2024:i:c:p:13-21
    DOI: 10.1016/j.insmatheco.2023.12.007
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    References listed on IDEAS

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    1. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    2. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    3. Jae Youn Ahn & Himchan Jeong & Yang Lu, 2023. "A simple Bayesian state-space approach to the collective risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(5), pages 509-529, May.
    4. Ou Dang & Mingbin Feng & Mary R. Hardy, 2020. "Efficient Nested Simulation for Conditional Tail Expectation of Variable Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(2), pages 187-210, April.
    5. Peng Shi, 2016. "Insurance ratemaking using a copula-based multivariate Tweedie model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(3), pages 198-215, March.
    6. Frangos, Nicholas E. & Vrontos, Spyridon D., 2001. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 1-22, May.
    7. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    8. Daniel H. Alai & Zinoviy Landsman & Michael Sherris, 2016. "Multivariate Tweedie lifetimes: the impact of dependence," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(8), pages 692-712, September.
    9. Lin, X. Sheldon & Yang, Shuai, 2020. "Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 85-103.
    10. Peng Shi & Gee Y. Lee, 2022. "Copula Regression for Compound Distributions with Endogenous Covariates with Applications in Insurance Deductible Pricing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1094-1109, September.
    11. Guojun Gan & Emiliano A. Valdez, 2018. "Regression Modeling for the Valuation of Large Variable Annuity Portfolios," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(1), pages 40-54, January.
    12. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    13. Ohlsson, Esbjörn & Johansson, Björn, 2006. "Exact Credibility and Tweedie Models," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 121-133, May.
    14. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    15. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
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    Cited by:

    1. Tianxing Yan & Yi Lu & Himchan Jeong, 2024. "Dependence Modelling for Heavy-Tailed Multi-Peril Insurance Losses," Risks, MDPI, vol. 12(6), pages 1-17, June.

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    More about this item

    Keywords

    Credibility premium; Dependence modeling; Multi-peril insurance; Posterior ratemaking; Tweedie distribution;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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