The Hermite model of mortality

(Jul 8, 2019)

In Richards (2012) I compared seventeen different parametric models for modelling the mortality of a portfolio of UK annuitants.  The best-fitting model, i.e. the one with the lowest AIC, was the Makeham-Beard model:

\[\mu_x = \frac{e^\epsilon+e^{\alpha+\beta x}}{1+e^{\alpha+\rho+\beta x}}\qquad(1)\]

where \(\mu_x\) is the force of mortality at age \(x\) and \(\alpha\), \(\beta\), \(\epsilon\) and \(\rho\) are parameters to be estimated.  These parameters have interpretations, e.g. \(\beta\) is broadly the rate at which the force of mortality increases by age on a logarithmic scale, \(e^\epsilon\) is the constant background rate of mortality and \(e^{-\rho}\) is the limiting force of mortality…

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Tags: Hermite splines, extrapolation

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