Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Mortality Improvement Models
Deterministic Models
1
...
0032
0
...
0037
0
...
An excerpt is:
X
54
55
56
57
𝜙(𝑥)
0
...
008
0
...
005
rd
Calculate the probability that a female age 54 in 2021 will die in the 3 year
...
0032(1 − 0
...
00317
𝑞(55, 2022) = 0
...
008)2 = 0
...
0037(1 − 0
...
00363
2|𝑞 (54, 2021) = (1 − 0
...
00335)(0
...
003610
2
...
0605 for a female in 2014
...
0211
0
...
0193
0
...
0172
Calculate q (80, 2018)
...
0605)(1 − 0
...
0193)(1 − 0
...
0172) = 0
...

𝑞(𝑥, 𝑦) = 𝑞(𝑥, 𝑦 − 1)(1 − 𝜙(𝑥, 𝑦))
𝑞(𝑥, 𝐵) = 𝑞(𝑥, 𝐴)(1 − 𝜙(𝑥, 𝐴 + 1))(1 − 𝜙(𝑥, 𝐴 + 2)) … (1 − 𝜙(𝑥, 𝐵))
3
...
Develop short term improvement factors
...
Then
𝑞̂(𝑥, 𝑡) = 𝑒 𝑠(𝑥,𝑡), and
𝑞̂(𝑥, 𝑡)
𝜙(𝑥, 𝑡) = 1 −
= 1 − 𝑒 𝑠(𝑥,𝑡)−𝑠(𝑥,𝑡−1)
𝑞̂(𝑥, 𝑡 − 1)

b
...

c
...

d
...
003
...
Spline interpolation
- For female age 80, improvement factors are 0
...
0195 in 2007
...
Initial slope is 0
...

𝑓(𝑡) = 𝑎𝑡 3 + 𝑏𝑡 2 + 𝑐𝑡 + 𝑑
𝑓(0) = 0
...
01
𝑓 ′ (𝑡) = 3𝑎𝑡 2 + 2𝑏𝑡 + 𝑐
𝑓 ′ (0) = 0
...
0018(20) + 0
...
01
12000𝑎 + 400𝑏 = −0
...
000006875
𝑏 = −0
...
000006875(133 ) − 0
...
0018(13) + 0
...
015543125



---