Page 18: solution to question on the top of the page in the notes. I think this sentence has some information omitted: In the random walk model, e(t) is the error term between the actual value of the increment (or increase) in the value of k(t) from its previous value k(t-1). This sentence is not very clear given the equation: k(t) - k(t-1) = mue(or average change in k(t)) + e(t) Is the sentence trying to imply that the error term is the difference between the actual value of increment and the average increase in k(t).
If I may add another question on the same chapter: page 32 the question based on the data on page 31. I understand what is done to get the new deaths over age 65. However, if the same method of adjusting deaths is applied to age 66, it results in a different measure of deaths calculated (2097*0.9=1887) than shown by adjusting q(66) (or adjusted q66=q66*0.9, then adjusted deaths = adjusted q66*adjusted lives alive at age 66=1890). So why have that difference of 1887 vs 1890? Any reason why one method should be preferred over the other (adjusting deaths vs. adjusting qx)?? Essentially both methods are being used but one for each year with no clear reasoning? I would have thought that qx is a computed figure whereas deaths are the pure observed values, and so better to begin with adjusting deaths as done for computing adjusted q65.
For the first question, see the corrected wording in the latest submission of corrections. For the second question, the method of d66 * 0.9 doesn't quite work - d66 is no longer 2097 under the "old death probabilities" once d65 has been updated for the cure. The calculation doesn't take into account the change in the lives at risk once the cure has had an impact at age 65. After adjusting at age 65 for the cure, l66_cure is now 77,450. If we apply the old death probability this would make d66 = 0.02711 * 77,450 = 2100. Now applying the adjustment to this updated "old" value we get d66 = 2100 * 0.9 = 1890 as the new number of deaths under the scenario. This is effectively applying the mortality rate of 0.02711 * 0.9 to the updated lives of 77,450 as indicated in the notes.
