Revision as of 22:27, 18 January 2024 by Admin (Created page with "For a select and ultimate mortality model with a one-year select period, you are given: (i) <math>\quad p_{[x]}=(1+k) p_{x}</math>, for some constant <math>k</math> (ii) <math>\quad \ddot{a}_{x: n}=21.854</math> (iii) <math>\quad \ddot{a}_{[x]: n]}=22.167</math> Calculate <math>k</math>. <ul class="mw-excansopts"><li> 0.005</li><li> 0.010</li><li> 0.015</li><li> 0.020</li><li> 0.025</li></ul> {{soacopyright|2024}}")
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AAdmin
Jan 18'24

Exercise

For a select and ultimate mortality model with a one-year select period, you are given:

(i) [math]\quad p_{[x]}=(1+k) p_{x}[/math], for some constant [math]k[/math]

(ii) [math]\quad \ddot{a}_{x: n}=21.854[/math]

(iii) [math]\quad \ddot{a}_{[x]: n]}=22.167[/math]

Calculate [math]k[/math].

  • 0.005
  • 0.010
  • 0.015
  • 0.020
  • 0.025

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

AAdmin
Jan 19'24

Answer: C

[math]\ddot{a}_{[x]: n]}=1+v p_{[x]} \ddot{a}_{x+1: n-1]}=1+(1+k)\left(v p_{x} \ddot{a}_{x+1: n-1}\right)=1+(1+k)\left(\ddot{a}_{x: n]}-1\right)[/math]

Therefore, we have

[math]k=\frac{\ddot{a}_{[x]: n]}-1}{\ddot{a}_{x: n]}-1}-1=\frac{21.167}{20.854}-1=0.015[/math]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

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