Case Study 2: Trends in Paid Losses vs Case Reserve Estimates

Comparing a model for the Paid Losses with a model for the Case Reserve Estimates can sometimes give additional information that could never be discovered from the Incurred Losses triangle. In this example, the Paid Losses have had a fairly steady calendar trend from 1991 to 2000, then it has accelerated somewhat since 2000. The picture in the Case Reserve Estimates is very different the trend is steady from 1989 to 1996, but then there is a sharp fall, followed soon after by a sharp rise. In the most recent years, the trend has decreased. When do you think this company was sold? The Case Reserve Estimates were dropping in the years just prior to the sale in 1998, then they had to climb again as the reserves were re-evaluated by the new owner. If you look instead at the cumulative Incurred Losses, and apply the regression equivalent of standard link ratios, the picture is much less clear. The model is significantly under-forecasting in the earliest and most recent accident years, and also in some of the more recent calendar years, but we cannot untangle the trend structure in the paid losses and case reserve estimates.

What has happened here?

Case Study 3: Assessing Your Existing Outward Reinsurance

Is your outward reinsurance giving you good value? Analysing your net and gross data together allows you to see the effects of the reinsurance clearly. In this example, the correlation is very high – 0.84. The pattern of trends is very similar in the development and accident directions, but the gross data has a calendar trend of 7% +- 2% per annum, whereas the calendar trend in the net data is not significantly different from zero. This suggests that the part of the paid losses that is growing has been ceded – the reinsurance is being effective. However, the net data has higher process variability than the gross data. The overall effect is that the total outstanding for the gross has a coefficient of variation of 15%, while the net has a coefficient of variation of 17%. This means that, as a percentage, the amount of capital above the mean has not been reduced by taking out this reinsurance. The cost of the reinsurance must also be considered, but it is likely that this is not a good outcome for theinsurer.

Similar Model Structure but different trends