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Dependence modeling in non-life insurance using the Bernstein copula

Author

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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.

Suggested Citation

  • 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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    7. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
    8. Bouezmarni, T. & Rombouts, J.V.K., 2009. "Semiparametric multivariate density estimation for positive data using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2040-2054, April.
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    Citations

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    Cited by:

    1. 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.
    2. Woo, Jae-Kyung & Cheung, Eric C.K., 2013. "A note on discounted compound renewal sums under dependency," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 170-179.
    3. 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.
    4. 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.
    5. 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.
    6. repec:eee:ecmode:v:67:y:2017:i:c:p:149-158 is not listed on IDEAS
    7. repec:eee:riibaf:v:45:y:2018:i:c:p:208-218 is not listed on IDEAS
    8. repec:eee:insuma:v:77:y:2017:i:c:p:38-48 is not listed on IDEAS
    9. Gregor Wei{ss} & Marcus Scheffer, 2012. "Smooth Nonparametric Bernstein Vine Copulas," Papers 1210.2043, arXiv.org.

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