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Meyers, Glenn G. 2007. “Estimating Predictive Distributions for Loss Reserve Models.” Variance 1 (2): 248–72.
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  • Figure 1. Distribution of insurer size
  • Figure 2. Empirical payment paths for accident year 1986: Incremental paid losses as a proportion of 10-year total
  • Figure 3. Empirical payment paths for the four industry segments
  • Figure 4. Limited average severity by settlement lag
  • Figure 5. Maximum likelihood estimates of incremental paid development factors
  • Figure 6. Maximum likelihood estimates of the ELR parameters
  • Figure 7. Sample p-p plots
  • Figure 8. P-P plot for the top 40 insurers
  • Figure 9. P-P plots for the top 40 insurers by settlement lag
  • Figure 10. P-P plots by settlement lag for insurers ranked 41–250
  • Figure 11. Comparing the selected prior distribution of ELR with the maximum likelihood estimates of ELR for the top 40 insurers
  • Figure 12. Predictive distribution of actual losses for total reserve, insurer rank 7
  • Figure 13. Predictive distribution of actual losses of total reserve, insurer rank 97
  • Figure 14. Predictive coefficient of variation plotted with the predictive mean for 250 insurers
  • Figure 15. P-P plot of predicted percentiles for paid losses from 1996 to 2001
  • Figure 16. Predictive percentiles of reported reserves
  • Figure 17. Analysis of subsequent reserve changes for 109 insurers

Abstract

This paper demonstrates a Bayesian method for estimating the distribution of future loss payments of individual insurers. The main features of this method are (1) the stochastic loss reserving model is based on the collective risk model; (2) predicted loss payments are derived from a Bayesian methodology that uses the results of large, and presumably stable, insurers as its prior information; and (3) this paper tests its model on a large number of insurers and finds that its predictions are well within the statistical bounds expected for a sample of this size. The paper concludes with an analysis of reported reserves and their subsequent development in terms of the predictive distribution calculated by this Bayesian methodology.