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A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving

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  • Benjamin Avanzi
  • Gregory Clive Taylor
  • Phuong Anh Vu
  • Bernard Wong

Abstract

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach. We consider factors that evolve across accident years in conjunction with factors that evolve across calendar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time. We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.

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  • Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    • Handle: RePEc:arx:papers:2004.06880
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    References listed on IDEAS

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    1. Piet de Jong, 2006. "Forecasting Runoff Triangles," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 28-38.
    2. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2019. "Calendar Year Effect Modeling For Claims Reserving In Hglm," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 763-786, September.
    3. Verrall, R.J., 1994. "A Method for Modelling Varying Run-Off Evolutions in Claims Reserving," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 325-332, November.
    4. 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.
    5. Peters, Gareth W. & Shevchenko, Pavel V. & Wüthrich, Mario V., 2009. "Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 1-33, May.
    6. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    7. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Model uncertainty in claims reserving within Tweedie's compound Poisson models," Papers 0904.1483, arXiv.org.
    8. 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.
    9. Brydon, D. & Verrall, R. J., 2009. "Calendar Year Effects, Claims Inflation and the Chain-Ladder Technique," Annals of Actuarial Science, Cambridge University Press, vol. 4(2), pages 287-301, September.
    10. Atherino, Rodrigo & Pizzinga, Adrian & Fernandes, Cristiano, 2010. "A Row-Wise Stacking of the Runoff Triangle: State Space Alternatives for IBNR Reserve Prediction," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 917-946, November.
    11. Shi, Peng & Frees, Edward W., 2011. "Dependent Loss Reserving using Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 449-486, November.
    12. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    13. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    14. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    15. Nataliya Chukhrova & Arne Johannssen, 2017. "State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing," Risks, MDPI, vol. 5(2), pages 1-23, May.
    16. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    17. Alai, Daniel H. & Wüthrich, Mario V., 2009. "Taylor Approximations for Model Uncertainty within the Tweedie Exponential Dispersion Family," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 453-477, November.
    18. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard, 2016. "Correlations Between Insurance Lines Of Business: An Illusion Or A Real Phenomenon? Some Methodological Considerations," ASTIN Bulletin, Cambridge University Press, vol. 46(2), pages 225-263, May.
    19. Ioannis Ntzoufras & Petros Dellaportas, 2002. "Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(1), pages 113-125.
    20. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    21. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    22. Saluz, Annina & Gisler, Alois, 2014. "Best estimate reserves and the claims development results in consecutive calendar years," Annals of Actuarial Science, Cambridge University Press, vol. 8(2), pages 351-373, September.
    23. 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.
    24. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard, 2018. "Common Shock Models For Claim Arrays," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1109-1136, September.
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    Cited by:

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    2. Yanez, Juan Sebastian & Pigeon, Mathieu, 2021. "Micro-level parametric duration-frequency-severity modeling for outstanding claim payments," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 106-119.

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