Effects of inflation
Key Points state: "A uniform inflationary pressure, τ, in general puts less pressure on claim sizes in excess of a lower limit A because not all of the claims below the limit A before inflation will be above A after accounting for inflation. This means the rate of inflation for excess claims is generally lower than the uniform inflation rate."
I dont quite get this - my understanding is claim previously above A will get the full increase by the inflation, but the lower limit A is unchanged, so the % increase in the excess layer is higher. In addition to that, there are some losses that are lower than A before inflation and now pierce limit A after inflation, further increase losses in excess layer.
How could the inflation for excess claims be lower than uniform inflation rate?
Reference: Past exam 2012 Question 22(c)
Comments
The key here is the terminology - excess claims is referring to the claim severity (size) rather than the aggregate loss. There are claim severities which even after applying inflation are still below the excess attachment point. This dampens the effect of claim size inflation in the excess layer.
See Example 5.10 in the source text for an illustration.
Past exam 2012 Q22 is referring to aggregate loss rather than severity when you're calculating the deductible LER.
Thanks, in the scenario where all claims exceed attachment point after inflation, will the claim size inflation in excess layer = ground up inflation?
Yes, this is equivalent to shifting the distribution so the ground up loss now corresponds to the attachment point for the excess layer.
Hi,
I would like to follow on this. I took a look at the example 5.10 in the source text, and I also get your point that there are claim severities which even after applying inflation are still below excess AP.
I tried to determine the impact by coming up with some numbers:
My calculations showed that the claim size inflation in the excess layer (i.e. inflation of excess severity based on example 5.10) is actually larger than the uniform inflation rate. Do you mind pointing out to me which part that I am missing??
Thanks!
Your calculations are correct. The statement you're testing only holds in general according to Bahnemann. Bahnemann is implicitly making this statement in the context of claim severity distributions which are usually heavily right skewed.
Your example shows zero to slightly negative skewness (left skewed) so isn't a fair representative of a claim severity distribution (especially with the small sample size).
Example 5.10 uses a Pareto distribution which is heavily right skewed. The first part demonstrates how inflation is dampened for claims in excess of 5,000 even though there is no upper limit.
By looking at the formula for the effective trend factor for excess claim severity, you see (for positive inflationary effects) the first two terms are greater than 1 while the last is less than 1. The interplay between the choice of limit, inflationary rate, and the shape of the distribution determine whether or not the excess claim severity inflation is greater than the ground up inflation.
thanks so much! this clarifies!