Q9: The examiners report says "Age retirement can be ignored in constructing the dependent decrements." Why? Is this always true? Thanks
I don't have the question in front of me, but I suspect they say this because in this case the member is assumed to retire (under normal situations) only at a single age, the NRA e.g. 60. This therefore doesn't interact with any of the other decrements before that age. This is likely to be the case in all exam questions. However, in reality, it may be assumed that there a probability of retiring at ages earlier than NRA as well, in which case you would not be able to ignore this in deriving the dependent decrements.
I think I get it now, thanks for your answer. The question gives a decrement of retiring of 0.2 at each age from 60 to 64 all exact. Then it says age retirements are assumed to take place on the attainment of the exact age, whilst other decrements act uniformly across the year of age. So the retirement decrement is not interacting with the other decrements up to the exact age, which is why the other decrements across each year of age aren't dependent on it. That sound right?
what about q13? So if it is true that "the retirement decrement is not interacting with the other decrements up to the exact age, which is why the other decrements across each year of age aren't dependent on it", how does this logic apply to question 13? Here, surrenders occur only at the end of a year, death benefit is paid only at the end of the year, but in the Examiner's Report (bottom of p.13) we have dependent q = independent q for death, but dependent q <> independent q for surrender. What's the story?? Cheers, R
Yes, that's correct. The retirements occur at the end of each year of age, and so don't interfere with the other decrements operating across each year of age. The Examiners Report shows the calculation of the dependent probability of surviving (death and IH retirement) over each year, up to just before the exact age at which retirement occurs. The (dependent) probability of retiring at the end of the year is obtained by multiplying this probability of surviving over the year by 0.2 (the probability of retiring at the end of the year). In Q13, the surrenders all occur at the end of the year and so do not interfere with the deaths that occur over the year. Over the year, then, only one decrement is operating (death), so the dependent and independent probabilities for death coincide. The (dependent) probability of surrendering at the end of the year is obtained by multiplying the probability of surviving death over the year by the probability of surrendering at the end of the year. So, I think this is the same approach as in Q9.
