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Dependence modelling in multivariate claims run-off triangles

Author

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  • Merz, Michael
  • Wüthrich, Mario V.
  • Hashorva, Enkelejd

Abstract

A central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

Suggested Citation

  • Merz, Michael & Wüthrich, Mario V. & Hashorva, Enkelejd, 2013. "Dependence modelling in multivariate claims run-off triangles," Annals of Actuarial Science, Cambridge University Press, vol. 7(1), pages 3-25, March.
    • Handle: RePEc:cup:anacsi:v:7:y:2013:i:01:p:3-25_00
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    Cited by:

    1. Alexeev Vitali & Ignatieva Katja & Liyanage Thusitha, 2021. "Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-20, April.
    2. Jonas Alm, 2015. "Signs of dependence and heavy tails in non-life insurance data," Papers 1501.00833, arXiv.org.
    3. Bohnert, Alexander & Gatzert, Nadine & Kolb, Andreas, 2016. "Assessing inflation risk in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 86-96.
    4. Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    5. Benjamin Avanzi & Gregory Clive Taylor & Bernard Wong & Xinda Yang, 2020. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Papers 2004.11169, arXiv.org, revised Dec 2020.
    6. 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.
    7. Badescu, Andrei L. & Lin, X. Sheldon & Tang, Dameng, 2016. "A marked Cox model for the number of IBNR claims: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 29-37.

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