Twin Peaks

(Jun 15, 2017)

If you are over forty, the title of this blog will call to mind an iconic, sometimes disturbing, television series of the same name from 1990.  If you clicked on the link expecting murder, surreal horror and an undercurrent of sleaze, however, then this posting is as far away from all that as you are ever likely to get: setting capital requirements for life insurers.  Take a deep breath to recover from your crushing disappointment and let's get back to the day job…

Insurers in the EU operate under Solvency II, which is a one-year, value-at-risk regulatory regime.  The idea is that an insurer needs to hold reserves which will be sufficient to cover 99.5% of adverse scenarios over the coming year and still have enough…

Read more

Tags: value-at-risk, bimodal distribution, Solvency II, model risk

Fifty years of mortality improvements

(Jun 2, 2017)

In an earlier post we looked at the development of the distribution of age at death over time.  We saw how the peak adult age at death had continuously moved towards an ever-higher age.

Actuaries, of course, are very interested in the development of mortality rates over time.  Animation 1 shows the development of the crude observed force of mortality for males of retirement age in the UK since 1961. It shows that mortality rates have fallen at all ages, but much more so at ages below 80 than above.

Animation 1. Male mortality rates by age in England and Wales since 1961 (log scale). Click on the chart to restart the animation. Note that the mortality rates were calculated using post-2001 population estimates that had…

Read more

Tags: mortality improvements

Universal Prescription

(May 26, 2017)

In April 2017 the UK Government unveiled its Cycling and Walking Investment Strategy (CWIS), the first binding legislation ensuring government investment in cycling and walking provision in England. CWIS commits 1.2 billion GBP of spending by 2020/2021, coming from central and local government as well as from local enterprise partnerships. While clearly falling within transport planning, and despite being less directly revenue-friendly than the recent UK tax on sugar sweetened beverages, it is appropriate to view CWIS as a public health initiative. Indeed the foreword to the policy cites better health and improved air quality among the benefits sought by doubling cycling activity by 2025.

We'll consider…

Read more

Tags: longevity, research, exercise, public health

Frailty models

(May 1, 2017)

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.

Let us suppose that Gompertz really was right and that the mortality of each individual follows their own Gompertz law from ages 40 to 90, say.  Notice that this is very different from saying that the mortality of the entire population (of individuals) follows the Gompertz law.  Let…

Read more

Tags: frailty

Changing patterns of mortality

(Apr 28, 2017)

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.

The development of the distribution of deaths by age can reveal a lot about a population.  Animation 1 shows the development of the distribution of deaths for males in England and Wales since 1961.  It shows the very welcome fall in infant mortality on the left, but it also shows the steady rightward drift in the distribution at older ages.

Animation 1. Male deaths by age in England and Wales since 1961.  Click on the chart to restart the animation.

ONS deaths by age for males in England and Wales since 1961

Animation 1 shows how the modal age at death drifts…

Read more

Tags: 1919, curve of deaths

On the (funding) level

(Apr 18, 2017)

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.  My amazement was reawakened recently when I received a statement about my preserved pension from a former employer.  An excerpt from the statement is shown below:

Table 1. Excerpt from summary funding statement.

  Actuarial valuation
as at
31 December 2013
Assets £2,904m
Estimated amount required
to provide benefits
Surplus/Deficit £330m
Funding level 113%


On the face of it,…

Read more

Tags: pension-scheme funding, expenses, market consistency

Special Delivery

(Apr 4, 2017)

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. Their "specific pain" range, despite bold claims on the packaging, was deemed to not target back pain, migraine or indeed any other specific pain. As a result, the premium pricing was ruled misleading and earned the company a AU$6 million fine. Pharmaceutical marketing departments will likely be unhappy that a regulator has decided the standard approach of deploying medication via simple blood circulation should no longer be represented as targeted.

Of course, this issue isn't simply about misleading…

Read more

Tags: mortality, cancer, targeting

The Alias Problem

(Mar 18, 2017)

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.  Members accruing benefits have a job classification (say), which can be used to model mortality differentials.  Let's assume the classification is M (manual) and O (office), and that this coding is available for all member pensioners.  Of course, pension schemes also contain benefits paid to surviving spouses, but unless they also worked for the same employer they won't have a job classification.  We therefore have a job-classification factor with three levels: M, O and S (for spouses).

Another common…

Read more

Tags: extrinsic aliasing

Top of the tree

(Feb 20, 2017)

What do civil servants and monkeys have in common (ignoring a purportedly greater than average interest in bananas)? This question isn't an invitation to heap scorn on the political establishment. After all, in these interesting times such an invitation seems hardly necessary. I'm referring, instead to the Whitehall studies, examining health and mortality outcomes for members of the British Civil Service. The original study began in 1968 and ran for a decade, while Whitehall II began in 1985. The findings from these prospective cohort studies continue to influence policy both nationally and internationally into the present day.

The central findings from Whitehall, however, still carry an element of…

Read more

Tags: mortality, social status, primates, monkeys

Division of labour

(Jan 10, 2017)

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: (i) the current, or period, mortality rates and (ii) the projection of the future path of mortality rates (usually mortality improvements).  This sub-division is carried over into the regular Solvency II assessment of capital requirements, where there is always a minimum of two sub-risks for longevity:

  1. Mis-estimation risk, i.e. the uncertainty over the current level of mortality.
  2. Trend risk, i.e. the uncertainty over the future direction of improvements.

In practice a Solvency II assessment…

Read more

Tags: Valuation, Solvency II, mis-estimation risk, trend risk

Older Posts »

Find by key-word

Find by date

Find by tag (show all )