DOI QR코드

DOI QR Code

Constrained Bayes and Empirical Bayes Estimator Applications in Insurance Pricing

  • Kim, Myung Joon (Department of Business Statistics, Hannam University) ;
  • Kim, Yeong-Hwa (Department of Applied Statistics, Chung-Ang University)
  • Received : 2013.04.29
  • Accepted : 2013.06.21
  • Published : 2013.07.31

Abstract

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

Acknowledgement

Supported by : Hannam University

References

  1. Louis, T. A. (1984). Estimating a population of parameter values using Bayes and empirical Bayes method, Journal of the American Statistical Association, 79, 393-398. https://doi.org/10.1080/01621459.1984.10478062
  2. Ghosh, M. (1992). Constrained Bayes estimation with applications, Journal of the American Statistical Association, 87, 533-540. https://doi.org/10.1080/01621459.1992.10475236
  3. Ghosh, M. and Kim, D. (2002). Multivariate constrained Bayes estimation, Pakistan Journal of Statistics, 18, 143-148.
  4. Ghosh, M., Kim, M. and Kim, D. (2008). Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function, Journal of Statistical Planning and Inference, 138, 2017-2028. https://doi.org/10.1016/j.jspi.2007.08.004
  5. Zellner, A. (1988). Bayesian analysis in econometrics, Journal of Econometrics, 37, 27-50. https://doi.org/10.1016/0304-4076(88)90072-3
  6. Zellner, A. (1992). Bayesian and non-Bayesian estimation using balanced loss functions, Statistical Decision Theory and Related Topics V, Springer-Verlag, New York, 377-390.

Cited by

  1. Bayes Risk Comparison for Non-Life Insurance Risk Estimation vol.27, pp.6, 2014, https://doi.org/10.5351/KJAS.2014.27.6.1017
  2. Application of Constrained Bayes Estimation under Balanced Loss Function in Insurance Pricing vol.21, pp.3, 2014, https://doi.org/10.5351/CSAM.2014.21.3.235