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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 function argument" founded 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 gives 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

 

 

 

 

 

...

...

 

 

 

 

 

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