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Combining Predictions of Auto Insurance Claims

Author

Listed:
  • Chenglong Ye

    (Dr. Bing Zhang Department of Statistics, University of Kentucky, 317 Multidisciplinary Science Building, 725 Rose St., Lexington, KY 40536, USA)

  • Lin Zhang

    (First American Financial, Santa Ana, CA 92707, USA)

  • Mingxuan Han

    (School of Computing, University of Utah, Salt Lake City, UT 84112, USA)

  • Yanjia Yu

    (School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA)

  • Bingxin Zhao

    (School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA)

  • Yuhong Yang

    (School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA)

Abstract

This paper aims to better predict highly skewed auto insurance claims by combining candidate predictions. We analyze a version of the Kangaroo Auto Insurance company data and study the effects of combining different methods using five measures of prediction accuracy. The results show the following. First, when there is an outstanding (in terms of Gini Index) prediction among the candidates, the “forecast combination puzzle” phenomenon disappears. The simple average method performs much worse than the more sophisticated model combination methods, indicating that combining different methods could help us avoid performance degradation. Second, the choice of the prediction accuracy measure is crucial in defining the best candidate prediction for “low frequency and high severity” (LFHS) data. For example, mean square error (MSE) does not distinguish well between model combination methods, as the values are close. Third, the performances of different model combination methods can differ drastically. We propose using a new model combination method, named ARM-Tweedie, for such LFHS data; it benefits from an optimal rate of convergence and exhibits a desirable performance in several measures for the Kangaroo data. Fourth, overall, model combination methods improve the prediction accuracy for auto insurance claim costs. In particular, Adaptive Regression by Mixing (ARM), ARM-Tweedie, and constrained Linear Regression can improve forecast performance when there are only weak learners or when no dominant learner exists.

Suggested Citation

  • Chenglong Ye & Lin Zhang & Mingxuan Han & Yanjia Yu & Bingxin Zhao & Yuhong Yang, 2022. "Combining Predictions of Auto Insurance Claims," Econometrics, MDPI, vol. 10(2), pages 1-15, April.
  • Handle: RePEc:gam:jecnmx:v:10:y:2022:i:2:p:19-:d:791038
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    References listed on IDEAS

    as
    1. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    2. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    3. Bailey, Robert A. & Simon, LeRoy J., 1960. "Two Studies in Automobile Insurance Ratemaking," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 192-217, December.
    4. Yang, Yuhong, 2004. "Combining Forecasting Procedures: Some Theoretical Results," Econometric Theory, Cambridge University Press, vol. 20(1), pages 176-222, February.
    5. Xinyu Zhang & Dalei Yu & Guohua Zou & Hua Liang, 2016. "Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1775-1790, October.
    6. Edward W. (Jed) Frees & Glenn Meyers & A. David Cummings, 2014. "Insurance Ratemaking and a Gini Index," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(2), pages 335-366, June.
    7. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
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