Credibility estimation via kernel mixed effects model

  • Shim, Joo-Yong (Department of Applied Statistics, Catholic University of Daegu) ;
  • Kim, Tae-Yoon (Department of Statistics, Keimyung University) ;
  • Lee, Sang-Yeol (Department of Statistics, Seoul National University) ;
  • Hwa, Chang-Ha (Department of Statistics, Dankook University)
  • Published : 2009.03.31

Abstract

Credibility models are actuarial tools to distribute premiums fairly among a heterogeneous group of policyholders. Many existing credibility models can be expressed as special cases of linear mixed effects models. In this paper we propose a nonlinear credibility regression model by reforming the linear mixed effects model through kernel machine. The proposed model can be seen as prediction method applicable in any setting where repeated measures are made for subjects with different risk levels. Experimental results are then presented which indicate the performance of the proposed estimating procedure.

Keywords

References

  1. Antonio, K. and Beirlant, J. (2008). Issues in claims reserving and credibility: a semiparametric approach with mixed models. Journal of Risk & Insurance, 75, 643-676. https://doi.org/10.1111/j.1539-6975.2008.00278.x
  2. Craven, P. andWahba, G. (1979). Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numerical Mathematics, 31, 377-403. https://doi.org/10.1007/BF01404567
  3. Dannenburg, D. R., Kaas, R. and Goovaerts, M. J. (1996). Practical actuarial credibility models, Institute of Actuarial Science and Econometrics, University of Amsterdam, Amsterdam, The Netherlands.
  4. Frees, E. W., Young, V. R. and Luo, Y. (1999). A longitudinal data analysis interpretation of credibility models. Insurance: Mathematics and Economics, 14, 229-247.
  5. Goovaerts, M. J. and Hoogstad, W. (1987). Credibility theory, surveys of actuarial studies. Journal of the American Statistical Associations, 57, 369-375.
  6. Hachemeister, C. A. (1975). Credibility for regression models with applications to trend. In Credibility: Theory and applications, Ed. P. M. Kahn, 129-163, Academic Press, New York.
  7. Hedeker, D. and Gibbons, R. D. (2006). Longitudinal data analysis, John Wiley & Sons, New York.
  8. Mercer, J. (1909). Functions of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society, A. 209, 415-446. https://doi.org/10.1098/rsta.1909.0016
  9. Valyon, J. and Horvath, G. (2005). A robust LS-SVM regression. Proceedings of World Academy of Science, Engineering and Technology, 7, 148-153, 2005.
  10. Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.