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($B$3) |
|
30 |
0.000377 |
=sActuarialGenerationalTableqxVector($F$3,$F$4,$F$5,$F$6) |
40 |
31 |
0.000401 |
|
|
31 |
0.000397792 |
|
41 |
32 |
0.000427 |
|
|
32 |
0.000420195 |
|
42 |
33 |
0.000454 |
|
|
33 |
0.000441852 |
|
43 |
34 |
0.000482 |
|
|
34 |
0.000463007 |
|
44 |
35 |
0.000514 |
|
|
35 |
0.000486345 |
|
45 |
36 |
0.00055 |
|
|
36 |
0.000511569 |
|
46 |
37 |
0.000593 |
|
|
37 |
0.000541097 |
|
47 |
38 |
0.000643 |
|
|
38 |
0.000574416 |
|
48 |
39 |
0.000701 |
|
|
39 |
0.000611849 |
|
49 |
40 |
0.000763 |
|
|
40 |
0.000655974 |
|
… |
... |
... |
|
|
... |
... |
|
Those resulting qx vectors can be used as the table inputs for a variety of actuarial routines, as showed in the example "Entering the qx vector directly as a function argument" found here.
Finally, you should notice that the entrance of an actuarial function can be facilitated through the options available in the Actuarial Toolbox tab. For instance, by selecting the option “Generational-2d (qx vector)” in the ”Table View” combo box you will get the following result:
A |
B |
C |
D |
E |
F |
G |
|
1 |
Generational 2d Table |
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
3 |
Actuarial table |
6 |
UP1994F |
|
|
|
|
4 |
First scale table number |
48 |
MP2014SCALE2015M |
|
|
|
|
5 |
Last scale table number |
63 |
MP2014SCALE2030+M |
|
|
|
|
6 |
Years from table |
0 |
|
|
|
|
|
7 |
Age |
30 |
|
|
|
|
|
8 |
|
|
|
|
|
|
|
9 |
Age (x) |
Probability of death (qx) |
|
|
|
|
|
10 |
0 |
0 |
|
|
|
|
|
11 |
1 |
0 |
|
|
|
|
|
12 |
2 |
0 |
|
|
|
|
|
13 |
3 |
0 |
|
|
|
|
|
14 |
4 |
0 |
|
|
|
|
|
... |
... |
... |
|
|
|
|
|
34 |
25 |
0 |
|
|
|
|
|
35 |
26 |
0 |
|
|
|
|
|
36 |
27 |
0 |
|
|
|
|
|
37 |
28 |
0 |
|
|
|
|
|
38 |
29 |
0 |
|
|
|
|
|
39 |
30 |
0.000377 |
={sActuarialGenerational2dTableqxVector($B$3,$B$4,$B$5,$B$6,$B$7)} |
|
|
|
|
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 |
|
|
|
|
|
… |
... |
... |
|
|
|
|
|