Most of our readers will normally associate the acronym FSA with the Financial Services Authority, the body supervising financial-services providers in the United Kingdom.  Confusingly, another UK regulator has the same acronym: the Food Standards Agency, which has nothing to do with financial services but is "an independent Government department [...] to protect the public's health and consumer interests in relation to food."

Recently the Food Standards Agency ran a campaign to warn people about hidden levels of salt in their food, especially pre-prepared foods.  New York City is running a similar health campaign.  This is because high salt intake is believed to play a role in certain diseases,…

Creating a good model from your experience data is not always straightforward. Data gathered over an extended time period, as financial portfolios usually are, will often incorporate artefacts from more than one administration system or servicing team, and it may require wide-ranging business experience to make the best analytical choices.

Perhaps for this reason, our clients often collaborate on modelling projects between offices and sometimes with external partners. At present, we know of one project involving analysts in both Canada and Bermuda, and another where the team spans no fewer than three organisations - two in France, and one in the UK. A server based approach makes such collaboration easier,…

Solvency II is a major overhaul of the reserving rules for insurers throughout the European Union.  An important consideration for annuity writers is how it will relate to longevity trend risk.  For example, consider the following text about "Statistical quality standards" as they refer to insurers' internal models:

Geodemographic profiles use addresses or postcodes to classify people into groups which are homogeneous with respect to variables like income, housing tenure and life stage.  The original purpose of geodemographic profiles was to improve targeting for marketing purposes.  There is no point in sending marketing material for hearing aids to young families, for example, and geodemographic profiles help make more efficient use of marketing resources.

Geodemographic profiles have been conclusively shown to be predictive of mortality in the United Kingdom, both by Richards (2008) and Madrigal et al (2009).  This is because geodemographic profiles are about education level, wealth and income (amongst…

In my previous post I illustrated the effects of over-dispersion in population data.  Of course, an actuary could quite properly ask: why use ONS data?  The CMI data set on assured lives might be felt to be a better guide to the mortality of pensioners, although Stephen has raised a question mark over this assumption in the past.

Figure 1 illustrates what happens with the CMI data set. The over-dispersion parameter is much smaller at 1.82, so the Poisson model gives a reasonable forecast.  Note that the over-dispersion in the CMI data comes from a different source, namely the presence of duplicates causing extra variability in death counts.  However, the same approach to over-dispersion works regardless of the…

Actuaries have a long-standing habit of using different terminology to statisticians.  This page lists some common terms used by actuaries in mortality work and their "translation" for a non-actuarial audience.  The terms and notation are those used by actuaries in the UK, but in every country I have visited the local actuaries have used similar notation.

Table 1. Common actuarial terms and their definition for statisticians.

Actuarial term	Actuarial notation	Statistical description
central exposed to risk		The time exposed to risk of dying at age x.
curve of deaths		Probability density function for the future lifetime of an individual currently alive and aged exactly x.
force of mortality		In…

Actuaries need to project mortality rates into the far future for calculating present values of pension and annuity liabilities.  In an earlier post Stephen wrote about the advantages of stochastic projection methods.  One method we might try is the two-dimensional P-spline method with the simple assumption that the number of deaths at age i in year j follows a Poisson distribution (Brouhns, et al, 2002).  Figure 1 shows observed and fitted log mortalities for the cross-section of the mortality surface for age 70 with this method.

Figure 1.  Observed log(mortality) rates with fitted P-spline for underlying average.  ONS data for males in England & Wales.

At first sight, all seems well - the fit seems perfectly…

When investigating risk in an annuity portfolio, a key task is to simulate the future lifetime for each annuitant.  Survival models make this particularly easy, as covered in an earlier posting on simulating lifetimes.

One of the first things which strikes practitioners is that volatility in run-off valuations increases with the average age of a portfolio.  The reason for this is that the variation in future lifetime gets larger relative to the average future lifetime.  One way of looking at this is to use the coefficient of variation, which is simply the standard error of the future lifetime divided by the mean:

coefficient of variation = standard error / mean

The coefficient of variation is normalised in that…

Love them or loathe them, actuaries cannot get by without standard tables in some shape or form. Even when performing analysis of your own experience data to avoid basis risk, standard tables are often used as a kind of lingua franca between parties, a convenient way to express approximate results in a way everyone can understand.

The use of standard tables in experience analysis brings its own issues of course: Mortality moves on after a table is published, and even those that are not too outdated may still be innappropriate for the population under study. In any case the rates from a standard table will often require significant transformation in order to achieve something vaguely similar to your actual experience.…

This month sees the twentieth anniversary of the fall of the Berlin Wall.  This is therefore an appropriate time to remind ourselves of a dramatic example of the plasticity of mortality.  This is the ability of mortality rates to change quickly in response to a new environment, particularly decreases in mortality.

The sudden and unexpected reunification of the two halves of Germany in 1989 provided demographers with an interesting sort of social experiment.  As Scholz and Maier (2003) put it: