Two key assumptions of the Mack model (from core reading of ST7 notes) are: - "The future development of a claim cohort is independent of the historical factors (eg. high factors in one period do not imply high or low factors in the following period)" - "the variance of the cumulative claims to development time t is proportional to the cumulative claims amount to time t-1" Does the 2nd statement contradict the first one? If I were to have very large cumulative claims at t-1 (compared to low cumulative claims at t-1, due to whatever may or may not have happened between t-2 and t-1), this is going to mean the variance of the cumulative claims at t is very large (compared to very small), which would imply higher chance of a higher development factor for period "t-1 to t". So how can we then say the future development of this cohort is independent of its history?
I think maybe the first assumption makes use of the mean of the development (since the Mack method is based on the Basic Chain Ladder) while the second assumption is all about the variance of the development. So these are two completely separate issues. Also, the variance of the cumulative claims to time t is assumed to depend on the cumulative claims amount at time t-1, but this doesn't imply that the variance at t depends on anything further back in the history and so it doesn't depend on the historical development factors.
Mack & Boot-strapped ODP September 2010, question 4iv compares these two methods. With respect to the Mack Method: Isn't "the future development of a claim cohort is independent of the historical factors" synonymous with stable claims development? incremental claim amounts being independent? Wouldn't "assume that the causes of uncertainty will be captured within historic data" apply to BCL as well? With respect to the bootstrapped ODP, an assumption is that the variance of incremental claim amounts is proportional to the mean - The mean of what? The mean of incremental claim amounts?
1. "The future development of a claim cohort is independent of the historical factors" is effectively synonymous with a stable claims development. However, this wouldn't necessarily mean that incremental claim amounts are independent. 2. "Assume that the causes of uncertainty will be captured within the historic data" would also apply to the BCL as well. Remember that the Mack Model reproduces the Chain Ladder estimates. For the ODP we are referring to the mean of the incremental claim amounts.
So just to confirm, "The future development of a claim cohort is independent of the historical factors" is also one of the assumptions of the CL method? Thanks
The key assumptions of the basic chain ladder method are shown in Section 2.1 of Chapter 13 as follows: Past is a good guide to the future You can estimate a tail factor for the oldest year with reasonable confidence Future inflation is a weighted average of past inflation
