A generational mortality table is a life table where the probability of death at a given age does not remain constant as the time goes by. There are two types of generational tables: a fixed scaled generational table (one-dimensional table) and a moving scaled generational table (two-dimensional table). A fixed scaled generational table takes one base table and one scale table containing one value per age to project the future probability of death. The moving scaled generational mortality table projects a base table using a scale table that varies with the projection time. The table below compares the projected death rates for a man at the age of 35 using a standard mortality table (UP 1994 - Female) and a one-dimensional generational table (UP 1994 - Female with 1994 Mortality Improvement Projection Scale AA - Female):
A
B
C
D
E
F
G
1
UP 1994 - Female
UP 1994 - Female + Scale AA
2
3
Actuarial table
6
UP1994F
Actuarial table
6
UP1994F
4
Scale table
12
SCALEAA1994F
5
Years from table
0
6
Age
30
7
8
Age (x)
Probability of death (qx)
Age (x)
Probability of death (qx)
9
0
0
0
0
10
1
0.000571
1
0
11
2
0.000372
2
0
12
3
0.000278
3
0
13
4
0.000208
4
0
14
5
0.000188
5
0
...
...
...
...
...
34
25
0.000313
25
0
35
26
0.000316
26
0
36
27
0.000324
27
0
37
28
0.000338
28
0
38
29
0.000356
29
0
39
30
0.000377
=sActuarialqxVector($B3ドル)
30
0.000377
=sActuarialGenerationalTableqxVector($F3,ドル$F4,ドル$F5,ドル$F6ドル)
40
31
0.000401
31
0.000397792
41
32
0.000427
32
0.000420195
42
33
0.000454
33
0.000441852
43
34
0.000482
34
0.000463007
44
35
0.000514
35
0.000486345
45
36
0.00055
36
0.000511569
46
37
0.000593
37
0.000541097
47
38
0.000643
38
0.000574416
48
39
0.000701
39
0.000611849
49
40
0.000763
40
0.000655974
...
...
...
...
...
Those resulting qx vectors can be used as the table inputs for a variety of actuarial routines, as showed in the example "Entering the qx vector directly as a function argument" found here.
Finally, you should notice that the entrance of an actuarial function can be facilitated through the options available in the Actuarial Toolbox tab. For instance, by selecting the option "Generational-2d (qx vector)" in the "Table View" combo box you will get the following result:
A
B
C
D
E
F
G
1
Generational 2d Table
2
3
Actuarial table
6
UP1994F
4
First scale table number
48
MP2014SCALE2015M
5
Last scale table number
63
MP2014SCALE2030+M
6
Years from table
0
7
Age
30
8
9
Age (x)
Probability of death (qx)
10
0
0
11
1
0
12
2
0
13
3
0
14
4
0
...
...
...
34
25
0
35
26
0
36
27
0
37
28
0
38
29
0
39
30
0.000377
={sActuarialGenerational2dTableqxVector($B3,ドル$B4,ドル$B5,ドル$B6,ドル$B7ドル)}
40
31
0.000395
41
32
0.000415
42
33
0.000435
43
34
0.000457
44
35
0.000482
45
36
0.000509
46
37
0.00054
47
38
0.000575
48
39
0.000615
49
40
0.000656
...
...
...