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April 2019 CM1B Q3

S

Salma

Member
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!
 
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