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Frailty models

A population consists of individuals, each with their own genetics, lifestyle, and yes, their very own force of mortality. National mortality data, such as held by the Office for National Statistics (ONS), are observed only at the population level and the variation in the force of mortality across individuals of the same age is forever hidden. The purpose of this blog is to show how we can attempt to model this hidden heterogeneity.

Written by: Iain CurrieTags: frailty

Changing patterns of mortality

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.
Written by: Stephen Richards

On the (funding) level

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. 
Written by: Stephen RichardsTags: pension schemes, expenses, market consistency

Special Delivery

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.
Written by: Gavin RitchieTags: mortality, cancer, targeting

The alias problem

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.
Written by: Stephen RichardsTags: extrinsic aliasing

Top of the tree

What do civil servants and monkeys have in common (ignoring a purportedly greater than average interest in bananas)?
Written by: Gavin RitchieTags: mortality, socio-economic group, primates, monkeys

Division of labour

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.
Written by: Stephen RichardsTags: valuation, Solvency II, mis-estimation risk, trend risk

Habit (re)forming

Behavioural risk factors such as smoking and excessive alcohol consumption are significant drivers of mortality and morbidity.
Written by: Gavin RitchieTags: mortality, smoking, alcohol

Season's Greetings to all our readers!

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

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

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

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

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

Written by: Stephen Richards

Signal or noise?

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):

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

Written by: Stephen RichardsTags: CMI, APCI, APC, Lee-Carter, Age-Period, smoothing