#### Gompertz Makeham "Law" of Mortality

The Gompertz-Makeham model is a parametric model of human mortality. It is a mathematical model which requires its parameters to be estimated. The parameters, of course, are estimated by fitting the model to emperical data.

The 'force of mortality' / 'hazard function' is:

where:

- A is independent of age (the makeham term)
- is an age dependent component that grows exponentially (the gompertz term)
- x is age

The Gompertz Makeham formula is only accurate between ages 30 and 80^{[1]}https://en.wikipedia.org/wiki/Gompertz%E2%80%93Makeham_law_of_mortality.

*Presumably parametric models with additional parameters are used to model the whole human lifetime?*

Forces of mortality can be turned into 1-year probabilities for use in a mortality rate table using:

*I wonder do actuaries in life offices use parametric models of mortality for practical purposes ? My experience has been to work with mortality tables only rather than program in a parametric formula.*

*In my earlier years as a trainee actuary i was conducting a thought experiment and wanted some mortality tables to "get a feel" for how asset shares with sum at risk component could develop change over time. Without a set of mortality tables to hand i produced a quick formula in Excel that modelled the Gompertz-Makeham formula and used this to simulate asset shares. *

*I wonder how closely the G-M model can replicate the mortality tables used in practice by life companies for pricing, reserving etc? The model has a simple form so presumably any parametric models used for reserving or pricing have additional parameters.*

References

It is a mathematical model which requires its parameters to be estimated. Should be. It is a mathematical model with parameters to be estimated.

produced a quick formula in Excel that modelled the Gompertz-Makeham formula and used this to simulate asset shares.

produced a quick Excel model of the Gompertz-Makeham formula to simulate asset shares.