Here is the nowcast

(Jan 6, 2022)

Everyone is familiar with the idea of a forecast. You have data on a phenomenon up to the current time, and want to forecast the phenomenon at some point in the future.  The most obvious example is the weather forecast, but forecasting is also required in pension and annuity work.  For example, when calculating reserves for pension payments, some kind of projection is required for future mortality improvements.

However, there are many situations where the phenomenon of interest is not known at the current time, but will be after a time lag.  Examples are Gross Domestic Product (GDP) and inflation statistics, which only become available a few months after the time point they refer to.  This is a problem for central…

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Tags: OBNR, reporting delays

'Twas the Night Before Christmas

(Dec 24, 2021)

The title of this blog is the opening of A Visit from St. Nicholas, a famous poem of disputed authorship.  One of the possible authors was Henry Livingston Jr, who had a habit of signing his other poems with a simple "R"A Visit From St. Nicholas was submitted anonymously, making it hard to determine who really wrote it.

And just what, you might wonder, does any of this have to do with mortality and longevity?  Well, Livingston had twelve children, two of whom had the same name: Henry Welles Livingston.  The first died in infancy, while the second was born the following year and named for his deceased older brother, a practice known as a necronym.

As it happened, the second Henry Welles Livingston died in his thirties,…

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Tags: centenarians, data validation

A spline primer

(Nov 19, 2021)

A spline is a mathematical function.  They are used wherever flexibility and smoothness are required, from computer-aided design and cartoon graphics, to the graduation of mortality tables (McCutcheon, 1974).  There are numerous different types of spline, but the most common is the spline proposed by Schoenberg (1964).  Figure 1 shows Schoenberg splines of degrees 0-3, all of which start in 2015:

Figure 1. Schoenberg (1964) splines of degree 0-3 with first non-zero value from 2015.

Figure 1 illustrates a number of properties of a single Schoenberg spline:

  • The splines are local functions, and take the value zero outside their domain.
  • The domain of a spline of degree \(bdeg\) spans \(bdeg+2\) knot points.

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Tags: splines

Actuarial cycle time

(Oct 21, 2021)

The ongoing COVID-19 pandemic has introduced millions of ordinary people to some basic aspects of epidemiology, such as the R number to measure the reproductive ability of a virus.  However, there is another aspect to virus reproduction that is possibly even more important: cycle time.  This was pointed out recently by the epidemiologist Larry Brilliant, when he described the Delta variant of SARS-Cov-2 as "the most infectious disease of our lifetimes":

Sometimes we think of measles or chickenpox as the most explosive. What people get wrong, including a lot of my friends, is that they're forgetting about the cycle time. The incubation period of measles and chickenpox are approximately two weeks. The Delta…

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Tags: productivity, software, parallel processing

Build versus buy

(Oct 2, 2021)

In an earlier blog I quoted extensively from "The Mythical Man-Month", a book by the distinguished software engineer Fred Brooks.  My blog was admittedly self-interested(!) when it cited arguments made by Brooks (and others) for when it makes sense to buy software instead of writing it yourself.  However in place of "buying" one could perhaps better write "externally source" - in addition to purchasing (or licensing) purpose-written software, one can also use freely available software.  A good example is R, which itself depends upon other third-party libraries of mathematical subroutines, such as BLAS and LAPACK.

The question of what to build oneself, and what to externally source, is related to the economic…

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Tags: software, ARIMA, survival models, left-truncation

(H)arms race

(Sep 13, 2021)

I'm not a fan of the hyperbolic use of military metaphors in civilian life.  However, in rare cases they do seem appropriate, and the ongoing SAR-Cov-2 pandemic provides an example.  After all, describing a worker as "front-line" seems justified when the occupation carries a materially increased risk of infection and death (SAGE, 2021).

It is often said of military campaigns that the first casualty of battle is your battle plan - the enemy does not stand still, but adapts.  Something similar can be said of the SARS-Cov-2 virus, which undergoes continual evolution in the face of all our efforts to combat it.  However, unlike historical viral pandemics like the Spanish Influenza of 1918-1920, we have some new…

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Tags: coronavirus

No Thanks for the Memory

(Sep 1, 2021)

That there is "no substitute for experience" is a truism, and one that is very tempting to apply wholesale to human immunity. Indeed, we previously touched upon an particular feature of the 1918 Spanish Flu outbreak, the so-called "W-shaped" mortality impact resulting in disproportionate fatalities amongst younger adults in the 20-40 range. Some researchers theorise that older adults must have experienced an earlier influenza infection and thus gained a key immunological advantage over those not around at that time. However, our truism meets a strong challenge with COVID-19. One of the clearest and most robust observations globally is that for those infected by SARS-COV-2, it sucks to be old.

The different…

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Tags: coronavirus, influenza, pandemic, immunosenescence

Modelling mortality shocks

(Aug 16, 2021)

The ongoing coronavirus pandemic has so far produced two mortality shocks in the UK and many other countries.  Unsurprisingly, the extra mortality is also visible in annuity portfolios.  Such mortality spikes create a challenge for actuaries - how do you model a portfolio's mortality experience when the period covered includes one or more pandemic shocks?

Actuaries analyse recent experience data to set a best-estimate basis (future trends or improvements are usually handled as a separate basis item).  However, the presence of a mortality shock creates a risk of upward bias (unless you want to assume that such mortality shocks will regularly re-occur).  One thought might be to remove all deaths with covid-19…

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Tags: coronavirus, mortality shock, season

Buy versus build

(Aug 9, 2021)

If you are in the business of pricing and managing longevity risk, you need software to help you perform your analysis. You have two choices:

  1. Buy in software purpose-written for the task, or
  2. Build the software yourself.

We have been in the business of selling the software in (1) since 2006, so I fall somewhat short of being a disinterested commentator.  However, regarding (2) I recently rediscovered one of the seminal texts on software engineering, namely "The Mythical Man-Month" by Frederick P. Brooks.  Here is what he has to say regarding the decision above:

The most radical possible solution for constructing software is not to construct it at all [...] Even at a cost of $100,000, a purchased piece of software…

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Tags: software

EDS - Enhanced Dedicated Servers

(Aug 4, 2021)

A large part of our service has tradtionally revolved around Dedicated Servers - parallelised instances of our applications running on multi-threaded platforms for a single license holder (in contrast our shared servers offer single-thread performance in a multi-tenant way to multiple license holders, a model that is suitable for only the least demanding use-cases). Our original dedicated server model developed at the beginning of our business, and it was entirely physical, running on Dell 1950 hardware offering a choice of four or eight cores (hardware threads). After we moved our production platform to a virtualised and replicated environment for improved resilience, we retained our four/eight…

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Tags: technology

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