Uncertainty

Combining Models

It may be appropriate to model the variability of the total reserve as a single item.  Alternatively, this may be inappropriate for the same reason that the deterministic modeling of a total reserve may be inappropriate – changes in mix of business mask the true nature of the underlying data.  As such, it is important to have ways of modeling different classes of business separately before combining them into a total.

When modeling deterministically, we can simply add together the reserves of each class.  This is because the deterministic model targets the best estimate reserve and the sum of best estimate reserves is itself a best estimate of the total.

Unfortunately, the situation is slightly more complex when modeling ranges of reserves.  The sum of 99th percentiles will tend to be considerably higher than the 99th percentile of the total.  This is because of diversification effects – a heavy loss in one class may be offset by better-than-expected results in another class. 

We have developed several techniques for combining reserves from separate parts of a business.  These range from straightforward correlations between years of business and classes of business through to more complex tail-dependencies, in which there is a high degree of correlation between very bad results but a high degree of independence between less severe results.

What is Reserving Uncertainty and why is it Important?
Calculating Uncertainty
Case Estimate and IBNR Uncertainty