Hi, Why do we take (t-1)(ap)x in profit signature, and not t(ap)x? Why isn't the probability of the t-th period also multiplied? Thanks for your help! Regards, Shyam
Hie, I think the reason behind it is that in profit signature; we need profit of policyholders who survived upto this year(or who paid prem this year as well) from the beginning of policy. So, if we take t(ap)x then it will exclude those policyholders who died current year; although they had also paid prem and so profit belongs to them as well. In order to avoid such miscalculation, we'll use (t-1)( ap)x to consider all the policyholders who were alive at beginning of time and contributed towards this profit. I think this is the reason, but if I am wrong then tutor, please help me as well. Regards, Shikha Agarwal
Yes, definition that reads.. profit vector - Cash flow each year for individual who survives for that year. the cost of death/surrender is calculated using \(_{t}\left(aq\right)^{i}_{x}\) probability that life will die/surrender in given year. Profit signature - gives cash flow for individual who survives for full policy duration since inception. So used \(_{t-1}\left(ap\right)_x\) calculated by multiplying survival probabilities at each age.
