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#1




From 2018 LTAM Supplementary Note, Example 5.1
For the endowment benefit why you cannot use the formula: A_bar45:10 = 1d*a_bar45:10 with the adjusted delta here. The explanation the author provided is even more confusing. Does anyone knows.
Thanks 
#2




That adjusted delta isn't the actual interest rate. It's the fake delta when you combine the .04 interest rate and the +.01 force of mortality. They do this to express the probability portions of the annuity using the unadjusted probabilities.
As for the official explanation, it's just a side commentary about how the adjusted force of delta alone can't be used to get the value of insurances. That A* you see on the lefthand side contains both the adjusted interest rate as well as the adjusted probabilities of death from the +.01 force of mortality. This is in contrast to the annuity side, which can exist using the adjusted interest rate and the unadjusted probabilities. Ex: (v*)(Px) = (v)(Px*). Notice how the probability components of the annuity don't change if you use the adjusted interest rate. However, (v^[K + 2])(Px*)(q[x + 1]*) DOES NOT equal (v^[K + 2]*)(Px)(q[x + 1]), since the adjusted interest can only transform Px* to the unadjusted form. The term insurance components in that insurance take the form of (v[k + 2]*)(Px)(q[x + 1]*), which is not the same as using only the adjusted interest rate, since the q term is also adjusted by the new force of mortality. If you are still having issues comprehending, then I would recommend you just memorize. Memorization is how everyone passes. Just ace the multiple choice and pull random shit out of your ass in the written answer section. Last edited by Liar; 08182018 at 10:11 PM.. 
#3




Thank you "Liar" for your explanation. I followed your argument but I am not getting the same answer as the book. For a*45:20 I am getting 12.571 but the book apparently got 12.89554.
Here are some details: a*45:20 = (Integral 0 to 20) of (v^t)(tp*45)dt with v^t=exp(ln(1.04)*t) and tp*45=exp(AtB*c^45*(c^t1)/ln(c)) with A=.00022+.01+ln(1.04), B=2.7*10^6, c=1.124. Using Wolfram Alpha I evaluated the integral to be 12.571. Do you see anything I am doing wrong here. 
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