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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[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.

     

    2 Comments
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    Christopher Paine
    Christopher Paine
    9 months ago

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

    Christopher Paine
    Christopher Paine
    9 months ago

    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.