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Mortality & longevity

Mortality: A over E

Why ‘A over E’?

‘A over E’ literally refers to ‘actual’ deaths divided by ‘expected’ deaths as a measure of how experience data compares with a mortality.

In practice, ‘A over E’ is often interpreted as meaning the whole statistical caboodle, which is how I’ll use it here.

In the previous article we defined experience data, variables and mortality with respect to that data, and the \(\text{A}\) (actual) and \(\text{E}\) (expected) deaths operators.

In this article we’ll put \(\text{A}\) and \(\text{E}\) to work.

Mortality: Measures matter

This is the first in a series of articles outlining mortality experience analysis fundamentals, by which I mean estimating the underlying mortality for individuals in a defined group (e.g. members of a pension plan) from mortality experience data.

This will be fairly technical, but I’ll aim

  • to be concise,
  • to pull out the key insights, including what does and doesn’t matter in practice, and
  • to map concepts one-to-one to the process of actually carrying out a mortality experience analysis or calibrating and selecting mortality models.

On contemporary mortality models for actuarial use

Stephen Richards’ and Angus Macdonald’s paper ‘On Contemporary Mortality Models for Actuarial Use’ (due to be discussed at the Institute of Actuaries on 24 October 2024) makes the case for the following in mortality experience analysis1:

  1. Use individual data if at all possible.

  2. Work in continuous time and use instantaneous mortality rates, i.e. μ rather than q.

  3. Consider mortality experience data as comprising a series of Bernoulli trials over infinitesimally small time periods.

The paper could be read as a polemic against actuaries who can’t help but think in terms of q and whose first instinct is to group all time and age-dependent data on annual grids. Which is fine by me – I agree with the thrust of the paper and, in particular, the above three points.

So, having welcomed the paper, I do have a few observations…