To reflect expected future mortality improvements, a mortality table can be adjusted using a projection scale containing rates of mortality improvement. The mortality table’s 𝑞𝑥 values are projected from the table’s base year to future years. The projection can be to a fixed valuation year (static projection) or to each future year (generational projection). The projection can be done as a function solely of age (one-dimensional), or by both age and calendar year (two-dimensional).
The Society of Actuaries has a good discussion of mortality improvement in these reports:
· Mortality Improvement Scale BB Report
· Questions and Answers Regarding Mortality Improvement Scale BB
Also see here for a good description of mortality tables, mortality improvement projection scales, and generational mortality from the State of Arkansas Insurance Commissioner.
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Note: |
The Society of Actuaries believes that 2D scales
are superior to 1D scales and represent the best estimate of future mortality
improvement. |
With a static mortality projection, a mortality table is
projected 𝑛 years from the table’s base
year to a future year using an
improvement scale that varies by age. The projected mortality rate 
at age 𝑥 is
determined by the following formula:
Where:
age
annual
rate of mortality improvement from the one-dimensional improvement scale for
age 𝑥
mortality
rate for age 𝑥 from a base mortality table
projected mortality rate at age 𝑥
1-Dimensional Generational Mortality Improvement
If the projection of the base rates involves using a
1-dimensional improvement scale that varies by age only, the generational
mortality rate 
for a person age 𝑥
in year 𝑦+𝑛 is determined by the
following formula:
Where:
valuation
year
age
at year 𝑦
annual
rate of mortality improvement from the one-dimensional improvement scale for
age 𝑥
mortality
rate at age 𝑥 from a base mortality table
as of year 𝑦
generational mortality rate at age 𝑥 in year 𝑦+𝑛
2-Dimensional Generational Mortality Improvement
If the projection of the base
rates involves using a 2-dimensional improvement scale that varies by age and
calendar year, the generational mortality rate 
for a person age 𝑥
in year 𝑦+𝑛 is determined by the
following formula:
Where:
valuation
year
age
at year 𝑦
annual
rate of mortality improvement from the two-dimensional improvement scale for
age 𝑥
in year 𝑦
mortality
rate at age 𝑥 from a base mortality table
as of year 𝑦
generational mortality rate at age 𝑥 in year 𝑦+𝑛