1. Abstract Institute of Insurance Science Ulm University
Model Blending SCOR Natural Catastrophe Group
Uncertainty is ever present in the insurance business, and despite relentless enhancements in data
gathering and processing power, it is still a large factor in risk modeling and assessment. Therefore
finding any possible approaches which reduce models uncertainties would be desirable.
Essentially, in the reinsurance industry, particularly Natural Catastrophe modeling, there is one
common approach for narrowing uncertainties called Model Blending. This method is the process of
combining results from two or more sources to get a customized risk estimate. Each source indicates
different views of risk for the set of insured exposure. For example in case of this project we use two
data sources (tables) provided by RMS and AIR worldwide. These tables are commonly called YLT,
stands for year loss table. Actually both data sets represent the simulation of losses for wind storms
but with some differences in end results. Our task is employing two given sources and try to find an
averaged model which reflects the information of both data sets. Here we implement two methods
called “Severity Blending” and “Frequency Blending” for combining two mentioned sources and
hopefully end up with one blended source. Please note that, we believe RMS table is more accurate,
hence we set it as our baseline table and all further adjustments will be applied on this table.
The first approach is severity blending by taking weighted average over the losses in both tables with
the same exceedance probabilities. The immediate question coming up is which averaging method is
better (i.e. Arithmetic average or Geometric average); and also what are the reasonable weights.
Actually no one knows the precise answer to the above questions. However this report provides some
clues for those questions. The second approach, which is called frequency blending, will take the
average over exceedance probabilities in both tables with the same losses. Please note that for finding
same losses there is no explicit solution, so we provide an approximation method to do so.
Basically the aim of two approaches (i.e. Severity and Frequency) is to determine a new blended YLT
table. As we already mentioned earlier, all changes will be applied on the baseline table (RMS); so
customized baseline table is nominated as our blended YLT. Therefore the final step is to change the
blended AEP table to blended YLT table. This task is complicated and even more pronounced for
Frequency method rather than Severity. We have found an explicit solution for changing AEP to YLT
through severity blending but no exact solution for Frequency blending. However some approximate
solutions are provided in the rest of report. By evaluating the final results we can come to the conclusion
that one could decrease the uncertainty of his models by using several sources. If we are inclined to
the first data source for instance, we can give more weight to the first data in averaging process. This
inclination could be due to the accuracy of data or any other criteria.
In a nutshell, we can conclude that a blending approach is a powerful tool for reducing the risk of
uncertainty but it cannot eliminate all risks included in insurer’s book. The results are highly sensitive
to the parameters. Therefore, sensitivity analysis is of great importance and can be used as leverage
for management decisions. As an improvement, one can do research on changing AEP to YLT in
frequency blending which is still an open question.