A
amused942
Member
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?
- "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?