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Dependence Modelling for Heavy-Tailed Multi-Peril Insurance Losses

Author

Listed:
  • Tianxing Yan

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

  • Yi Lu

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

  • Himchan Jeong

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

Abstract

The Danish fire loss dataset records commercial fire losses under three insurance coverages: building, contents, and profits. Existing research has primarily focused on the heavy-tail behaviour of the losses but ignored the relationship among different insurance coverages. In this paper, we aim to model the aggregate loss for all three coverages. To study the pairwise dependence of claims from all types of coverage, an independent model, a hierarchical model, and some copula-based models are proposed for the frequency component. Meanwhile, we applied composite distributions to capture the heavy-tailed severity component. It is shown that consideration of dependence for the multi-peril frequencies (i) significantly enhances model goodness-of-fit and (ii) provides more accurate risk measures of the aggregated losses for all types of coverage in total.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jrisks:v:12:y:2024:i:6:p:97-:d:1416036
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    References listed on IDEAS

    as
    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. Liang Hong & Ryan Martin, 2018. "Dirichlet process mixture models for insurance loss data," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(6), pages 545-554, July.
    3. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    4. Kahadawala Cooray & Chin-I Cheng, 2015. "Bayesian estimators of the lognormal–Pareto composite distribution," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(6), pages 500-515, August.
    5. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
    6. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.
    7. Jeong, Himchan, 2024. "Tweedie multivariate semi-parametric credibility with the exchangeable correlation," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 13-21.
    8. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    9. Wang, S., 1994. "Premium Calculation by Transforming the Layer Premium Density," Working Papers 030, Risk and Insurance Archive.
    10. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    Full references (including those not matched with items on IDEAS)

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