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Modelling Dependence in Insurance Claims Processes with Lévy Copulas

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  • Avanzi, Benjamin
  • Cassar, Luke C.
  • Wong, Bernard

Abstract

In this paper we investigate the potential of Lévy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Lévy copula models. Through the introduction of new Lévy copulas and comparison with the Clayton Lévy copula, we show that Lévy copulas allow for a great range of dependence structures. Procedures for analysing the fit of Lévy copula models are illustrated by fitting a number of Lévy copulas to a set of real data from Swiss workers compensation insurance. How to assess the fit of these models with respect to the dependence structure exhibited by the dataset is also discussed. Finally, we provide a decomposition of the trivariate compound Poisson process and discuss how trivariate Lévy copulas model dependence in this multivariate setting.

Suggested Citation

  • Avanzi, Benjamin & Cassar, Luke C. & Wong, Bernard, 2011. "Modelling Dependence in Insurance Claims Processes with Lévy Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 575-609, November.
    • Handle: RePEc:cup:astinb:v:41:y:2011:i:02:p:575-609_00
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    Cited by:

    1. Shah, Anand, 2016. "Pricing and Risk Mitigation Analysis of a Cyber Liability Insurance using Gaussian, t and Gumbel Copulas – A case for Cyber Risk Index," MPRA Paper 111968, University Library of Munich, Germany.
    2. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.
    3. J. L. van Velsen, 2012. "Parameter estimation of a Levy copula of a discretely observed bivariate compound Poisson process with an application to operational risk modelling," Papers 1212.0092, arXiv.org.
    4. Vladimir Panov, 2017. "Series Representations for Multivariate Time-Changed Lévy Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 97-119, March.
    5. Nicole Bauerle & Gregor Leimcke, 2021. "Bayesian optimal investment and reinsurance with dependent financial and insurance risks," Papers 2103.05777, arXiv.org.
    6. Ragnar Levy Gudmundarson & Manuel Guerra & Alexandra Bugalho de Moura, 2021. "Minimizing ruin probability under dependencies for insurance pricing," Papers 2108.10075, arXiv.org.
    7. 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.
    8. Guo, Nan & Wang, Fang & Yang, Jingping, 2017. "Remarks on composite Bernstein copula and its application to credit risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 38-48.
    9. R.L. Gudmundarson & M. Guerra & A. B. de Moura, 2021. "Minimizing Ruin Probability Under Dependencies for Insurance Pricing," Working Papers REM 2021/0193, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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