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Application of a Vine Copula for Multi-Line Insurance Reserving

Author

Listed:
  • Himchan Jeong

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

  • Dipak Dey

    (Department of Statistics, University of Connecticut, 215 Glenbrook Rd. U-4120, Storrs, CT 06269-4120, USA)

Abstract

This article introduces a novel use of the vine copula which captures dependence among multi-line claim triangles, especially when an insurance portfolio consists of more than two lines of business. First, we suggest a way to choose an optimal joint loss development model for multiple lines of business that considers marginal distribution, vine copula structure, and choice of family for each pair of copulas. The performance of the model is also demonstrated with Bayesian model diagnostics and out-of-sample validation measures. Finally, we provide an implication of the dependence modeling, which allows a company to analyze and establish the risk capital for whole portfolio.

Suggested Citation

  • Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:111-:d:432602
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    References listed on IDEAS

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    1. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2015. "Modeling Dependence Between Loss Triangles With Hierarchical Archimedean Copulas," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 577-599, September.
    2. Jeong, Himchan, 2020. "Testing For Random Effects In Compound Risk Models Via Bregman Divergence," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 777-798, September.
    3. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    4. Rubén Albeiro Loaiza Maya & Jose Eduardo Gomez-Gonzalez & Luis Fernando Melo Velandia, 2015. "Latin American Exchange Rate Dependencies: A Regular Vine Copula Approach," Contemporary Economic Policy, Western Economic Association International, vol. 33(3), pages 535-549, July.
    5. Braun, Christian, 2004. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 399-423, November.
    6. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    7. Benedikt Schamberger & Lutz F. Gruber & Claudia Czado, 2017. "Bayesian Inference for Latent Factor Copulas and Application to Financial Risk Forecasting," Econometrics, MDPI, vol. 5(2), pages 1-23, May.
    8. Peters, Gareth W. & Dong, Alice X.D. & Kohn, Robert, 2014. "A copula based Bayesian approach for paid–incurred claims models for non-life insurance reserving," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 258-278.
    9. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    10. F. Louzada & P. H. Ferreira, 2016. "Modified inference function for margins for the bivariate clayton copula-based SUN Tobit Model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2956-2976, December.
    11. Peng Shi & Lu Yang, 2018. "Pair Copula Constructions for Insurance Experience Rating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 122-133, January.
    12. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    13. Zhang, Yanwei, 2010. "A general multivariate chain ladder model," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 588-599, June.
    14. Jose Arreola Hernandez & Shawkat Hammoudeh & Duc Khuong Nguyen & Mazin A. M. Al Janabi & Juan Carlos Reboredo, 2017. "Global financial crisis and dependence risk analysis of sector portfolios: a vine copula approach," Applied Economics, Taylor & Francis Journals, vol. 49(25), pages 2409-2427, May.
    15. Nagler, T. & Bumann, C. & Czado, C., 2019. "Model selection in sparse high-dimensional vine copula models with an application to portfolio risk," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 180-192.
    16. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    17. Goh, Gyuhyeong & Dey, Dipak K., 2014. "Bayesian model diagnostics using functional Bregman divergence," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 371-383.
    18. Shi, Peng & Frees, Edward W., 2011. "Dependent Loss Reserving using Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 449-486, November.
    19. Michael Merz & Mario Wüthrich, 2008. "Prediction Error of the Multivariate Chain Ladder Reserving Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 175-197.
    20. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
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    Cited by:

    1. Anja Breuer & Yves Staudt, 2022. "Equalization Reserves for Reinsurance and Non-Life Undertakings in Switzerland," Risks, MDPI, vol. 10(3), pages 1-41, March.
    2. Saeide Sefidi & Mojtaba Ganjali & Taban Baghfalaki, 2022. "Analysis of ordinal and continuous longitudinal responses using pair copula construction," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 255-280, August.
    3. Yixing Zhao & Rogemar Mamon & Heng Xiong, 2021. "Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17: a new paid-incurred chain approach to risk adjustments," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.

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