Information Matrix

In an earlier post we introduced the idea of the so-called curve of deaths, which is simply the distribution of age at death.  This is intimately bound up with survival models and the idea of future lifetime as a random variable.

When I read Allan Martin's earlier blog on how pension-scheme reserves routinely fail to include expenses, I was so surprised I had to ask him if it was really true.  As a former life-insurance actuary, any reserve which didn't include an allowance for expenses simply wasn't a complete assessment of the liability in my view. 

Drug molecules, without special intervention, don't apply only where we want them to. Indeed, late last year this fact landed pharmaceutical giant Reckitt Benckiser in trouble with the Australian regulator.

A problem that can crop up during mortality modelling is that of aliasing, specifically extrinsic aliasing.  The situation can be illustrated by an example of the sort of data available for a pension scheme.

What do civil servants and monkeys have in common (ignoring a purportedly greater than average interest in bananas)?

At this time of year insurers have commenced their annual valuation of liabilities, part of which involves setting a mortality basis.  When doing so it is common for actuaries to separate the basis into two components.

Behavioural risk factors such as smoking and excessive alcohol consumption are significant drivers of mortality and morbidity.

\[y = \frac{\log_e\left(\frac{x}{m}-sa\right)}{r^2}\]

\[\Rightarrow yr^2 = \log_e\left(\frac{x}{m}-sa\right)\]

\[\Rightarrow e^{yr^2} = \frac{x}{m}-sa\]

\[\Rightarrow me^{yr^2} = x-msa\]

\[\Rightarrow me^{rry} = x-mas\]

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):

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

Historical research we discussed previously proposed that significant increases in average life expectancy would require the cure of multiple diseases of aging. Without considering the detail of cause-of-death calculations conducted more than two decades ago, it certainly seems implausible even now that we'll cross such a dramatic Rubicon in the near-term.