I think it is best to say here that in my method for this I separate out the reserves at the start and end of year for my calculation, rather than calculating an 'increase in reserves' in total as in the notes. We did this on tutorial and it made it a little easier for me to understand on the day (though maybe due to current confusion, that wasn't really the case). In the Q&A bank for section 3, question 16, we are given the 'reserves at end of year per policy'. When I initially attempted this question, I took these to be reserves at the end of the year in my profit testing table. However, the solutions appear to use the reserve at end of year 1 from the question as my profit test table equivalent of the reserves at the start of year 2, and then calculate the reserve at the end of year one as p multiplied by this. etc. I'm really confused as to why this is the case. Are these reserves in the question the equivalent of x_V's? If so, am I interpreting them incorrectly in using them as reserves at the end of year x? Or is this to do with profit tests being calculated per policy in force at the start of the year? I hope this makes some sort of sense - but it has been really difficult to type out coherently - feel free to ask for more info if needed!
Hi KDarwin, Very difficult to explain this over email, especially as you appear to be presenting it all differently to the way I would teach it - I promise it's the same method. Profit Vector is profits at the end of the year per policy in force at the beginning of the year. So, let's say we are in Year 3 (Time 2 to Time 3) KEY PRINCIPLE: Everyone is alive at the start of year 3 (think of it as magic)! The money we have in the bank is the reserve at time 2 (2V)- there is no probability attached to this because everyone is alive. This rolls up with interest. This is the money we have. What do we need? Well, we need the reserve at time 3 (3V) for any policy that survives Year 3. So, multiply this by the probability that a life who is definitely alive at time 2, survives until time 3. This is the money we need. So, inc in reserves at time 3 = the money we need - the money we have and this contributes to profit vector. However, we can't just do "magic" and not worry about it. It's not necessarily true that everyone is alive at the start of Year 3. So, we deal with it by going from profit vector to profit signature by multiplying the probability a life alive at time 0, gets to time 2. I do hope this helps and good luck! John
