Looking at part (v) where you calculated the expected claims after a year. The examiners solutions look at the difference of the development at point 2015 and at point 2014 and apply this difference to the ultimate claim at that point. I am not sure if this is the correct way. For example if we take the figures in 2009: Ultimate is 118.8 % dev at end of 2014 is 71.59% % dev at end of 2015 is 88.89% So example solutions do 118.8 * (88.89% - 71.59%) = 21 in the next year. However, I am not sure why this is the correct way to do it. Surely we need to take a look at the IBNR remaining, and how much development has happened in that one year? I.e. the IBNR in 2011 is: 118.8 - 78 = 40.8 From 2014 to 2015, as a proportion the additional development that has happened is (88.89% - 71.59%) / (100% - 71.59%) = 60.9%, i.e. we expect 60.9% of the IBNR to flow through in the next 12 months. So the expected position is then 40.8 * 60.9% = 25 I don't understand the logic with examiners approach, so I am wondering if this approach is wrong somehow.
I think you are referring to part (vi) (a) of the question and not part (v). Also your example appears to be based on the 2011 u/w year and not the 2009 u/w year. If the estimated ultimate claims were based on the chain ladder method, then your method and the examiners approach would give the same answer as they are algebraically the same. The only reason they give different answers is because the estimated ultimate claims are based on the BF Method and not the chain ladder method. I expect that the examiners would have given you suitable credit whichever approach you took, provided you explained it clearly and stated any assumptions made.
