IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp257-268.html
   My bibliography  Save this article

Modelling extreme claims via composite models and threshold selection methods

Author

Listed:
  • Wang, Yinzhi
  • Hobæk Haff, Ingrid
  • Huseby, Arne

Abstract

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of insurance claim data. This paper discusses several composite models with commonly used bulk distributions, combined with a 2-parameter Pareto distribution above the threshold. We have explored how several threshold selection methods perform when estimating the reserve as well as the effect of the choice of bulk distribution, with varying sample size and tail properties. To investigate this, a simulation study has been performed. Our study shows that when data are sufficient, the empirical rule has the overall best performance in terms of the quality of the reserve estimate. The second best are either the square root rule or the exponentiality test. The latter works better when the right tail of the data is extreme. As the sample size becomes small, the best performance is obtained with simultaneous estimation. Further, the influence of the choice of bulk distribution seems to be rather large, especially when the distribution is heavy-tailed. Moreover, it shows that the empirical estimate of p≤b, the probability that a claim is below the threshold, is more robust than the theoretical one.

Suggested Citation

  • Wang, Yinzhi & Hobæk Haff, Ingrid & Huseby, Arne, 2020. "Modelling extreme claims via composite models and threshold selection methods," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 257-268.
  • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:257-268
    DOI: 10.1016/j.insmatheco.2020.02.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300251
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2020.02.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    3. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    4. Ana Cebrián & Michel Denuit & Philippe Lambert, 2003. "Generalized Pareto Fit to the Society of Actuaries’ Large Claims Database," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 18-36.
    5. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    6. Pigeon, Mathieu & Denuit, Michel, 2011. "Composite Lognormal-Pareto model with random threshold," LIDAM Reprints ISBA 2011020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. George Tzougas & Himchan Jeong, 2021. "An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount," Risks, MDPI, vol. 9(1), pages 1-17, January.
    2. Tzougas, George & Jeong, Himchan, 2021. "An expectation-maximization algorithm for the exponential-generalized inverse Gaussian regression model with varying dispersion and shape for modelling the aggregate claim amount," LSE Research Online Documents on Economics 108210, London School of Economics and Political Science, LSE Library.
    3. Girish Aradhye & George Tzougas & Deepesh Bhati, 2024. "A Copula-Based Bivariate Composite Model for Modelling Claim Costs," Mathematics, MDPI, vol. 12(2), pages 1-17, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    2. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    3. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    4. Sonia Benito & Carmen López-Martín & Mª Ángeles Navarro, 2023. "Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT)," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-31, March.
    5. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    6. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    7. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    8. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    9. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2023. ""Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant Unconditional Variance in Heavy-Tailed Time Series"," IREA Working Papers 202309, University of Barcelona, Research Institute of Applied Economics, revised Jul 2023.
    10. Chan, Ngai-Hang & Lee, Thomas C.M. & Peng, Liang, 2010. "On nonparametric local inference for density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 509-515, February.
    11. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2012. "Statistical Inferences for Generalized Pareto Distribution Based on Interior Penalty Function Algorithm and Bootstrap Methods and Applications in Analyzing Stock Data," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 173-193, February.
    12. Danielsson, Jon & Ergun, Lerby M. & Haan, Laurens de & Vries, Casper G. de, 2016. "Tail index estimation: quantile driven threshold selection," LSE Research Online Documents on Economics 66193, London School of Economics and Political Science, LSE Library.
    13. Wagner, Niklas & Marsh, Terry A., 2005. "Measuring tail thickness under GARCH and an application to extreme exchange rate changes," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 165-185, January.
    14. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    15. Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
    16. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    17. Koning, A.J. & Peng, L., 2005. "Goodness-of-fit tests for a heavy tailed distribution," Econometric Institute Research Papers EI 2005-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, vol. 139(2), pages 318-339, August.
    19. Chin, Wen Cheong, 2008. "Heavy-tailed value-at-risk analysis for Malaysian stock exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4285-4298.
    20. Alfarano, Simone & Lux, Thomas, 2010. "Extreme value theory as a theoretical background for power law behavior," Kiel Working Papers 1648, Kiel Institute for the World Economy (IfW Kiel).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:257-268. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.