### 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…