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Ch12 mortality projection question

C

CHUN LEONG LEE

Keen member
Hello there, i refer to page 18 of chapter 12 - mortality projection.

I refer to the table k^_t and b^_x. Could i get some guidance on how the formula is used to calculate these 2 values please, as I got kinda stuck here.

Thank you!
 
Hello

The kt have been calculated using the formula given on the bottom of page 17. For example:

k_2010^ = -4.34281 - (-4.37407) + -4.19971 - (-4.22093) + -4.04555 - (-4.06010) + -3.93223 - (-3.94915) + -3.86323 - (-3.87621) + -3.72970 - (-3.74264) = 0.10987

Once we have all the kt^, we can use the formula on page 17 for the estimates of b_x (equation (1)). For example:

b_60^ = [0.10987 * (-4.34281 - (-4.37407)) + 0.02228 * (-4.36458 - (-4.37407)) + -0.01532 * (-4.38363 - (-4.37407)) + -0.04805 * (-4.38925 - (-4.37407)) + -0.06878 * (-4.39006 - (-4.37407)) ] / (0.10987^2 + 0.02228^2 + (-0.01532)^2 + (-0.04805)^2 + (-0.06878)^2) = 0.28332

This is slightly off to what is in the notes (0.28334) as I've used rounded values here and exact values were used in the calculations in the notes.

Hope this helps!

Andy
 
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