Fall 2019 Q22 a)

Comments

• Graham

  July 2023

  I'm not sure I understand your question. What you described is what they did. The steps are:

  • calculate the triangle of ratios of S/S to paid claims (which they did)
  • develop this triangle of S/S ratios to ultimate to get an ultimate S/S ratio for 2018 (which they did)
  • multiply the ultimate S/S ratio for 2018 (calculated in the previous step) by the ultimate claim amount for 2018 to get the ultimate S/S amount for 2018 (which they did)
  • then subtract the 2018 paid S/S from the 2018 ultimate S/S amount to get the 2018 unpaid S/S (which they did)

  If I didn't answer your question, please specify which step of the solution (with numbers) you think is incorrect.
• judyoh

  July 2023

  I am confused about bullet point 3. "Multiply the ultimate S/S ratio for 2018 by the ultimate claim amount..." because in the solution, it says that the 2018 ultimate ratio (0.1619) appears too low so instead they take an average of the 2015-2017 ultimate ratios to get 0.221 and instead use this as the ultimate ratio used in calculating the unpaid S/S.

  Is there a judgemental step in this method? Why is the solution stating that the 2018 ultimate ratio appears low and using a different value for the calculation?
• Graham

  August 2023

  There is always a certain amount of judgment when estimating ultimates. In other words there is no single correct answer. Sample answer 1 could have used the calculated value of 0.1619. They simply chose not to for the reason outlined below...

  When the development method is applied to the triangle of ratios, we get ultimate S/S ratios for each of the years 2015-2018. Sample answer 1 assumes that these S/S ultimate ratios should be consistent from year to year, which is a reasonable assumption unless you specifically know that something changed in 2018. Here, the ratio for 2015-2017 is roughly 0.221 whereas the ratio for 2018 is much lower at 0.1619, so the person assumes that the value of 0.1619 is due to random fluctuation and is not representative of the "true" S/S ratio so they don't use it.

  As an alternative, It would also have been acceptable to average the calculated S/S values for the years 2015-2018, which works out to 0.206 and use that instead of 0.221 to complete the problem.