# Learning Center

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 … ... ...