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Dependence modeling in non-life insurance using the Bernstein copula

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  • Diers, Dorothea
  • Eling, Martin
  • Marek, Sebastian D.

Abstract

This paper illustrates the modeling of dependence structures of non-life insurance risks using the Bernstein copula. We conduct a goodness-of-fit analysis and compare the Bernstein copula with other widely used copulas. Then, we illustrate the use of the Bernstein copula in a value-at-risk and tail-value-at-risk simulation study. For both analyses we utilize German claims data on storm, flood, and water damage insurance for calibration. Our results highlight the advantages of the Bernstein copula, including its flexibility in mapping inhomogeneous dependence structures and its easy use in a simulation context due to its representation as mixture of independent Beta densities. Practitioners and regulators working toward appropriate modeling of dependences in a risk management and solvency context can benefit from our results.

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  • Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:3:p:430-436
    DOI: 10.1016/j.insmatheco.2012.02.007
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    References listed on IDEAS

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    2. Eling, Martin & Jung, Kwangmin, 2020. "Risk aggregation in non-life insurance: Standard models vs. internal models," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 183-198.
    3. Juan Wu & Xue Wang & Stephen G. Walker, 2014. "Bayesian Nonparametric Inference for a Multivariate Copula Function," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 747-763, September.
    4. Shahid Latif & Slobodan P. Simonovic, 2022. "Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(14), pages 5599-5632, November.
    5. Dodo Natatou Moutari & Hassane Abba Mallam & Diakarya Barro & Bisso Saley, 2021. "Dependence Modeling and Risk Assessment of a Financial Portfolio with ARMA-APARCH-EVT models based on HACs," Papers 2105.09473, arXiv.org.
    6. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    7. Marri, Fouad & Moutanabbir, Khouzeima, 2022. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 75-90.
    8. Jens Stange & Taras Bodnar & Thorsten Dickhaus, 2015. "Uncertainty quantification for the family-wise error rate in multivariate copula models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 281-310, July.
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    10. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    11. Jonas Alm, 2015. "Signs of dependence and heavy tails in non-life insurance data," Papers 1501.00833, arXiv.org.
    12. Ming-Chu Chiang & I-Chun Tsai, 2016. "Ripple effect and contagious effect in the US regional housing markets," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(1), pages 55-82, January.
    13. Ming-Chu Chiang & I-Chun Tsai, 2016. "Ripple effect and contagious effect in the US regional housing markets," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(1), pages 55-82, January.
    14. Mejdoub, Hanène & Ben Arab, Mounira, 2018. "Impact of dependence modeling of non-life insurance risks on capital requirement: D-Vine Copula approach," Research in International Business and Finance, Elsevier, vol. 45(C), pages 208-218.
    15. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.
    16. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
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    19. Gregor Wei{ss} & Marcus Scheffer, 2012. "Smooth Nonparametric Bernstein Vine Copulas," Papers 1210.2043, arXiv.org.

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