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#### 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

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

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