2016 Fall Q26 (b)
Hi,
The solution compared the paid ULAE inflation (year over year change) to the paid claims inflation and conclude that the approach is inappropriate.
Could you elaborate more on how does comparing loss cost trend and paid ULAE trend relate to the stability assumption?
stability assumption: the ratio (paid ULAE) / (paid claims) is stable and reasonably approximates the ratio (ultimates ULAE) / (ultimate claims)
Thank you!
Comments
Recall the formula for unpaid ULAE where the IBNR is all pure IBNR or IBNYR:
and the formula for the ULAE ratio:
The ULAE ratio is normally calculated using several years, let's say from 2016 to 2020. That's because there can be random variation in the ratio for single years, and using a multi-year average smooths it out. In any case, we're assuming the "true" underlying ULAE ratio is the same for each year, and that it will be the same going forward. If you apply the calculated ULAE ratio to 2021, you should get the correct unpaid ULAE.
But if paid ULAE and paid claims have different rates of inflation then the underlying ULAE ratio for each year will not be the same. In the exam problem you referenced, paid ULAE is increasing at 10% per year whereas paid claims are only increasing at 2% per year. That means the ULAE ratio is actually increasing over time. If you apply the calculated ULAE ratio to 2021, assuming inflation continues at the same rates, your ULAE ratio will be too small for 2021 and you will under-estimate the unpaid ULAE.