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Quantifying the risk using copulae with nonparametric marginals

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  • Bolancé, Catalina
  • Bahraoui, Zuhair
  • Artís, Manuel

Abstract

We show that copulae and kernel estimation can be mixed to estimate the risk of an economic loss. We analyze the properties of the Sarmanov copula. We find that the maximum pseudo-likelihood estimation of the dependence parameter associated with the copula with double transformed kernel estimation to estimate marginal cumulative distribution functions is a useful method for approximating the risk of extreme dependent losses when we have large data sets. We use a bivariate sample of losses from a real database of auto insurance claims.

Suggested Citation

  • Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    • Handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:46-56
    DOI: 10.1016/j.insmatheco.2014.06.008
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    References listed on IDEAS

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    Cited by:

    1. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    2. 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.
    3. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
    4. Bolancé, Catalina & Vernic, Raluca, 2019. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 89-103.
    5. Catalina Bolancé & Raluca Vernic, 2017. "“Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution”," IREA Working Papers 201718, University of Barcelona, Research Institute of Applied Economics, revised Oct 2017.
    6. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
    7. Catalina Bolancé & Montserrat Guillén & Alemar Padilla, 2015. "Estimación del riesgo mediante el ajuste de cópulas," Working Papers 2015-01, Universitat de Barcelona, UB Riskcenter.
    8. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.

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