This is always a stumbling point... Profit vector = profits at end of year per pol in force at START OF THAT YEAR. So, if we are in year 3, everyone is alive at time 2, the beginning of Year 3 (think of it as magic). So, the money we have is 2V rolled up with interest. The money we need is 3V multiplied by the probability of surviving Year 3. Cost of inc reserves = money we need minus money we have. Now, this is all very well but what about the magic? Actuaries don't usually like magic. We prefer logic and reality. So, we calculate profit signature = profits at end of year per pol in force at START OF THE CONTRACT = profit vector * prob a life survives to start of that year. Give it another go and good luck! John
OK, let's do Year 2 and you can do the others. I've copied and pasted my advice from above, so that you can see exactly how it applies to Question 13.10 Profit vector = profits at end of year per pol in force at START OF THAT YEAR. So, if we are in year 2, everyone is alive at time 1, the beginning of Year 2 (think of it as magic). So, the money we have is 1V rolled up with interest. In Question 13.10, this is one year’s office premium rolled up at 7%. So, 1.07P is the money that we have The money we need is 2V multiplied by the probability of surviving Year 2. In Question 13.10, this is one year’s office premium * p61. So (1-0.009009)P is the money that we need. Cost of inc reserves = money we need minus money we have. 0.990991P - 1.07P = - 0.079009P Good luck! John
