Information Matrix

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):

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

When using a stochastic model for mortality forecasting, people can either use penalty functions or time-series methods . Each approach has its pros and cons, but time-series methods are the commonest. I demonstrated in an earlier posting how an ARIMA time-series model can be a better representation of a mortality index than a random walk with drift.

An important quantity in mathematical statistics is the moment of a distribution, i.e. the expected value of a given power of the observations. Moments can be either raw, centred about a particular value or standardised in some way. The simplest example is the mean of a distribution: this is the raw first moment, i.e. the expected value of each observation raised to the power 1:

Predicting the exact impact of weight upon mortality has proven to be a tricky business. That obesity is on the rise is universally acknowledged, but in recent years we have seen research studies reach differing conclusions, depending on the populations examined and the measures used.

In a previous posting I looked at how using a well founded statistical model can improve the accuracy of estimated mortality rates. We saw how the relative uncertainty for the estimate of \(\log \mu_{75.5}\) could be reduced from 20.5% to 3.9% by using a simple two-parameter Gompertz model:

\(\log \mu_x = \alpha + \beta x\qquad (1)\)