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For example, MPTF models will allow you to decide whether your current outward reinsurance program is effective, and help you to
design an optimal outward reinsurance program. See Case Study 3 for an example where the benefits of outward reinsurance are assessed. By looking at the residual plots, fitted trends and correlations provided by ICRFS-PLUS™, you can assess what segments are or are not related. The residuals to the right, plotted against calendar year, come from different categories of payments under a Workers’ Compensation policy. The trends have been removed in the development and accident directions, but not in the calendar direction. The two segments are clearly highly correlated the correlation coefficient is 0.7. If the statistically significant trends in the calendar direction are removed, the correlation drops to 0.4, so there is still residual correlation after all trends have been removed. In the example below, there are six layers of paid losses. Adjacent layers have correlations of 0.3-0.5. The correlation decreases as the layers become further apart, finally becoming not significantly different from zero. Correlation between layers (or the lack of it) could affect the benefits from reinsurance. The multiple triangle model in ICRFS-PLUS™ allows you to take into account both the correlation between trends and the correlation between residuals, to give you the best possible estimate of the combined risk of the segments. Often the same model can be used, with minor adjustments, for a number of different segments. The differences in the models will help you understand how the segments differ. Has social inflation been higher in one than the other? Is the final development trend flatter, leading to a longer tail of payments? Which segment has more process variability? |
Payments for Deafness |
Payments for Asbestosis |
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Credibility Modelling |
There are only two main applications of credibility modelling:
In the first case, if you have any related triangles – another company's data, industry data – that extends over a longer period, you can model these related triangles together and use the development and calendar trends in the larger triangle to credibility adjust the trends in the smaller triangle. Note that we do not credibility adjust process variability the companys process variability is not related to the industrys process variability or that of any other company. In the second case, one approach is to look at the industry data. Because the whole industry has a much larger exposure than your company alone, the process variability is likely to be much smaller. This makes it easier to identify any shifts in trends. Using the multiple triangle model in ICRFS-PLUS™, it is easy to combine the information from both your company and the industry. Just model them both and let the correlations speak for themselves. If the relationship between the two is strong enough, the credibility effect will automatically reduce the uncertainty in your companys trend estimates. |
Company process varibility is very high |
Industry process variability is low |