I'm writing to ask about the workings of a practice question in Chapter 17. In question 17.8, it is assumed that force of mortality between consecutive integer ages is constant. Why does miu has to be calculated? It can be taken from the Tables. Also, tpx is calculated as e^(-miu t). Although I understand this, I'm wondering why we don't just use tpx = (px)^t? Thanks.
Hi, We never use mu from the tables because that represents the force of mortality at an exact age x. For example, mu_50 is the force of mortality at the instant of age 50 but by age 50.00001 it will have changed. Hence, we have to calculate a constant mu that's equivalent to the one year-survival probability px. You could use tpx = (px)^t but I think this would make the integration more challenging (with integration by parts?). We can avoid that by writing it in exponential form and combining it with the discount factor. Hope this helps. Thanks Joe
