Large claims

A conventional approach to the treatment of large claims involves determining a threshold for such claims, using this threshold to divide the experience into "large" and "other", and analysis of the two cohorts separately.

This approach has several shortcomings, not the least of which is the arbitrariness of the segmentation. Further disadvantages include:

• The complexity of interactions between the two models as claims move between "large" and "other";
• Clustering of case estimates;
• Sparseness of large claim data, making trend analysis difficult;
• Truncation of the claim distribution, making stochastic modelling difficult; and
• Often, an increase in overall valuation uncertainty, concentrated in the large claim liability.

It is quite likely that the large claims form a longer tailed distribution than the smaller claims. This can be easily tested by sampling each cohort and examining the tails of the sampled distributions. If this is the case, an alternative approach is to not separate large and small claims, but to apply a claim size transformation to the data, such that all transformed claims sizes appear to come from a single sampling distribution. This will tend to reduce the size of larger claims relative to smaller ones.

Once this is done, the valuation can be completed on the transformed data set. An inverse transformation is subsequently applied to the results, and a final adjustment is then made for any bias created by the transformation process.