Hi can someone please explain the approach taken to construct the table for the dependent rates of death and surrender. Why isn't this formula being used to calculate (aq) d x & (aq) s x: eg: (aq) d 45= (0.00124/(0.075+0.00124)) * (1-e^-(0.075+0.00124)) Thanks!
The surrender decrement is not continuously active on the population. Instead, policyholders only have the opportunity to surrender at the end of each year. (aq)_x^d is therefore = q_x^d as mortality is the only continuously active decrement over a given year of age. If a policyholder is active at the start of a year of age, x, then they must survive that year in order to surrender at the end of it. So we calculate (aq)_x^s = (1 - q_x^d) * P(surrender at end of year). Note also that if each decrement was active over the year, then you'd need to use forces of decrement (mu_x^d and mu_x^s) in the formula you've suggested, rather than the q_x probabilities. CM1B September 2019 Q1 (ii) tests this knowledge, so it's a good one to take a look at!
