Everything points to Poisson

(Jan 16, 2018)

One recurring theme in our forthcoming book, Modelling Mortality with Actuarial Applications, is the all-pervading role of likelihoods that suggest the lurking presence of a Poisson distribution.  A popular assumption in modelling hazard rates is that the number of deaths observed at any given age is a Poisson random variable, so perhaps that might explain it?  Surprisingly, it is the other way round - it is the very nature of the data in a survival model that leads inexorably to the Poisson distribution, even if we assume no such thing.

Stripped back to basics, we observe \(n\) individuals and record our observations as:

  • The length of time \(E_i\) that the \(i\)th person was observed and alive; and
  • An indicator…

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Tags: survival data, Poisson distribution

Mortality by the book

(Dec 22, 2017)

Our book, Modelling Mortality with Actuarial Applications, will appear in Spring 2018.  I wrote the second of the three parts, where I describe the modelling and forecasting of aggregate mortality data, such as provided by the Office for National Statistics, the Human Mortality Database or indeed by any insurer whose own data is suitable.  I have divided my contribution into four chapters. In the first chapter I deal with one-dimensional data, for example, deaths by age for a given year.  The Gompertz model is used to introduce the regression-based approach; estimation is initially by least squares, but by the end of the chapter I use generalized linear models (GLMs) with both Poisson and binomial errors.

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Tags: GLMs, mortality projections, R

Risk transfer...and transfer risk

(Dec 21, 2017)

The risk-transfer market for defined-benefit pensions in the UK has been  buoyant for many years.  There is considerable demand from pension schemes - to say nothing of their sponsoring employers - for solutions that transfer risks to insurers.  These risk transfers can be comprehensive, such as bulk annuities that take on investment, inflation and all demographic risks.  Or else they can be narrowly focused, such as the longevity swaps that only transfer a specific part of a scheme's overall risk.

Whatever the solution, something else needs to be transferred long before the risk can be: data.  To price a longevity swap or a bulk annuity, an insurer or reinsurer needs some very specific data on the lives covered. …

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Tags: personal data, postcodes, security, Excel

Age rating

(Nov 17, 2017)

Back in the days before personal computers, actuaries relied solely on published tables for their calculations.  These were not just the mortality tables, but monetary functions of these tables known as commutation factors.  My old student tables from 1980 list commutation and other factors at discount rates of 4%, 6% and 8% (the latter rate seems almost comically high by current standards).  If you wanted to use a different discount rate, you would have to perform the same calculation twice and interpolate.

However, actuaries couldn't interpolate if they wanted to use higher or lower mortality rates - all monetary functions were calculated using a fixed (and implied) 100% of the rates in the stated mortality…

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Tags: age rating, Makeham-Beard

Priority Clearance

(Nov 14, 2017)

We previously discussed the clearance of senescent cells as a plausible treatment for multiple diseases of aging. The theory goes that senescent cells drive systemic inflammation, and that this inflammation underlies aging pathology. In August 2017 the latter part of this theory was underscored by results from the CANTOS study. These showed the addition of the anti-inflammatory ACZ885 reduced major adverse cardiovascular events by 15% above the best available standard care, and also appeared to bring a 50% reduction in cancer mortality for patients on the higher dose. However, suppressing inflammation with ACZ885 carried a stark downside: a significant increase in the risk of fatal infections that…

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Tags: longevity, research, inflammation, disease

How much data do you need?

(Aug 30, 2017)

There are two common scenarios when an actuary has to come up with a mortality basis for pensioners or annuitants:

  1. For a portfolio of liabilities already owned, e.g. an insurer's existing annuities in payment or a pension scheme's pensions in payment.
  2. For a portfolio of liabilities where the risk is to be transferred, e.g. an insurer or reinsurer looking to price a buy-out or longevity swap.

Leaving aside questions of data quality, in each case the actuary is faced with the same question: is the portfolio's experience data large enough to rely on? And if there isn't enough experience data, what does the actuary do instead?

At one extreme consider a pension scheme with a hundred pensioners. With an average of around…

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Tags: credibility, basis risk, concentration risk

Of Mice and (Space)Men

(Jul 20, 2017)

It may seem obvious, but when encountering longevity research, it bears repeating: human biology is not mouse biology. For this reason, one of my resolutions for 2017 was to minimise blogs centered around rodents. But longevity science, much like Disney, finds functioning without the mouse more or less unthinkable. Our recent foray into the world of monkeys, was only delaying the inevitable. When it became obvious that mice were turning the wheel, not just for medical progress, but also towards the stars, well, I realised there's always 20181.

DNA damage has been found to accumulate with advancing age. This is unsurprising. Since simple sunlight and other aspects of our environment are considered mutagenic,…

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Tags: mortality, longevity, DNA, mice

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…

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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…

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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…

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Tags: longevity, research, exercise, public health

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