Signal or noise?

(Nov 25, 2016)

Each year since 2009 the CMI in the UK has released a spreadsheet tool for actuaries to use for mortality projections.  I have written about this tool a number of times, including how one might go about setting the long-term rate.  The CMI now wants to change how the spreadsheet is calibrated and has proposed the following model in CMI (2016a):

\[\log m_{x,y} = \alpha_x + \beta_x(y-\bar y) + \kappa_y + \gamma_{y-x}\qquad (1)\]

which the CMI calls the APCI model.  \(m_x\) is the central rate of mortality at age \(x\) in year \(y\) and \(\alpha_x\), \(\beta_x\), \(\kappa_y\) and \(\gamma_{y-x}\) are vectors of parameters to be estimated.  \(\bar y\) is the average year, which is used to centre the time index around…

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Tags: CMI, APCI, APC, Lee-Carter, Age-Period, smoothing


(Nov 28, 2012)

Graduation is the process whereby smooth mortality rates are created from crude mortality rates.  Smoothness is an important part of graduation, but another is the extrapolation of mortality rates to ages at which data may be unreliable or even non-existent.  An example would be pension-fund work where reliable mortality-experience data might be available up to age 100, but where actuaries required mortality rates up to age 120 (say) for the purposes of calculating pension reserves.  An illustration of this dual smoothing and extrapolation is given in Figure 1.

Figure 1. log(mortality) by age for males in United States of America.  Crude rates shown for ages 20-100, together with graduated rates outside…

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Tags: graduation, extrapolation by age, smoothing, splines

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