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Forecasting aggregate claims using score‐driven time series models

Author

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  • Mariana Arozo B. de Melo
  • Cristiano A. C. Fernandes
  • Eduardo F. L. de Melo

Abstract

In the insurance industry, premium estimation and ruin probability valuation depend fundamentally on the aggregate claims distribution. From the mathematical point of view, the aggregated claims variable is a random sum of random variables. Obtaining the analytical expression for its probability distribution is a hard task. In this paper, a new approach is proposed for the modeling of the aggregated claims predictive distribution. The newly proposed generalized autoregressive score models are combined to specify non‐Gaussian distributions for both the number of claims and the claims severity. In all models, appropriate parameters were made time varying according to a score‐driving mechanism. By the use of the fast Fourier transform, we are then able to numerically obtain the aggregated claims distribution. The proposed method is applied to real data, provided by a Brazilian motor insurer.

Suggested Citation

  • Mariana Arozo B. de Melo & Cristiano A. C. Fernandes & Eduardo F. L. de Melo, 2018. "Forecasting aggregate claims using score‐driven time series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 354-374, August.
    • Handle: RePEc:bla:stanee:v:72:y:2018:i:3:p:354-374
    DOI: 10.1111/stan.12139
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    References listed on IDEAS

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    1. F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
    2. Drew Creal & Bernd Schwaab & Siem Jan Koopman & Andr� Lucas, 2014. "Observation-Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 898-915, December.
    3. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    4. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    5. Blasques, Francisco & Koopman, Siem Jan & Łasak, Katarzyna & Lucas, André, 2016. "In-sample confidence bands and out-of-sample forecast bands for time-varying parameters in observation-driven models," International Journal of Forecasting, Elsevier, vol. 32(3), pages 875-887.
    6. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Leena Kalliovirta, 2012. "Misspecification tests based on quantile residuals," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 358-393, June.
    9. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.
    10. Chaubey, Yogendra P. & Garrido, Jose & Trudeau, Sonia, 1998. "On the computation of aggregate claims distributions: some new approximations," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 215-230, December.
    11. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    12. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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