On Page 28 of Chapter 14 I can't understand the explanation as to why the method fails when the development factors is less than 1. Can someone provide a detail explanation with an example. Cheers
I don't know if fails is the right word but it is 'inappopriate' because it suggests that the reduction in ultimate (CDF being less than 1) is a function of the premium/lr rather than the incurred amount.
Yes, quite right. Just to give you a bit more help on this if you're not very familar with "downward development" or the BF method ... If dev factors are less than one, this means that for most origin years (i.e. each row in the triangle), claims incurred in some dev years will be greater than the ultimate claims. This is likely to be due to the case estimates of outstanding claims being too over-estimated. [Remember, claims incurred are (pretty much) claims paid + case estimates]. As the claim cohort develops, the (too big) case estimates are replaced by the actual claims paid, and so the claim incurred figure reduces. If this has happened in previous years, we'll expect it to happen in future years, and the development factors will reflect this. Using the BF method, on a claim cohort where reductions in claims incurred are expected, the estimate of future claims is a negative percentage, but the problem is that we apply this to the initial estimate (IE); we really want to apply it to the claims developed to date. So using BF if, for example, the IE is high (e.g. becuase the underwriter expect a high loss ratio), we make a big reduction, leading to a smaller estimate of the ultimate loss - the opposite of what we want! We'd be better off using basic chain ladder and ignoring the underwriter's estimate! The numerical exercise in Q&A bank Question 4.12 gives a worked example and more detail on this; suggest you work through this. We also discuss this in the ST3 tutorials. Hope this helps. Steve
