Reference Material

 "Mortality shocks and reporting delays in portfolio data" (2021) by Richards, S. J., Longevitas Working Paper
 "Modelling mortality by continuous benefit amount" (2020) by Richards, S. J., Longevitas Working Paper
 "A value-at-risk approach to mis-estimation risk" (2020) by Richards, S. J., Longevitas Working Paper
 "Modelling seasonal mortality with individual data" (2020) by Richards, S. J., Ramonat, S. J., Vesper, G. and Kleinow, T., Scandinavian Actuarial Journal (to appear)
 "A Hermite-spline model for post-retirement mortality" (2019) by S. J. Richards, Scandinavian Actuarial Journal, 2019, pages 1-18
 "Mis-estimation risk: measurement and impact" (2016) by S. J. Richards, British Actuarial Journal, 21(3), pages 429-475 (including discussion)
 "Creating portfolio-specific mortality tables: a case study" (2013) by S. J. Richards, K. Kaufhold and S. Rosenbusch, European Actuarial Journal, 3(2), pages 295-319
 "A handbook of parametric survival models for actuarial use" (2012) by S. J. Richards, Scandinavian Actuarial Journal, 2012(4), pages 233-257
 "Setting the proportion-married assumption" (2008) by S. J. Richards, Longevitas Technical Note
**Only available to licence-holders of our software products.
 "Improving annuity pricing with address data" (2008) by S. J. Richards, Life and Pensions magazine, September 2008
**Only available to licence-holders of our software products.
 "Applying survival models to pensioner mortality data" (2008) by Richards, S. J., Presented to Sessional Meeting of Institute of Actuaries, February 25th 2008
 "Modelling pensioner longevity" (2007) by Richards, S. J., Life and Pensions magazine, May 2007
**Only available to licence-holders of our software products.
 "Understanding pensioner longevity" (2007) by Richards, S. J., The Actuary magazine, November 2007
The editorial team of The Actuary chose this as its article of the month in November 2007.**Only available to licence-holders of our software products.
 "Pricing demographic risks in bulk buy-outs" (2006) by Richards, S. J.,
**Only available to licence-holders of our software products.
 "Anti-selection and annuity pricing" (2005) by Robinson, D. and Richards, S. J., The Actuary magazine, May 2005
**Only available to licence-holders of our software products.
 "Survey of annuity operations" (2005) by Richards, S. J., Richards Consulting
**Only available to licence-holders of our software products.
 "Financial aspects of longevity risk" (2004) by Richards, S. J. and Jones, G. L., Staple Inn Actuarial Society
This paper was listed as one of the top five papers every life actuary should know about at the 2006 Life Convention.
 "Longevity in the 21st Century" (2004) by Willets, R. C, Gallop, A. P., Leandro, P. A., Lu, J. L. C., Macdonald, A. S., Miller, K. A., Richards, S. J., Robjohns, N., Ryan, J. P. and Waters, H. W., British Actuarial Journal, 10, IV, 695--898
This paper won two prizes: one from the Faculty of Actuaries and another from the Institute of Actuaries
 "Longevity trend risk over limited time horizons" (2019) by S. J. Richards, I. D. Currie, T. Kleinow and G. P. Ritchie, Annals of Actuarial Science, 1-16, doi:10.1017/S174849952000007X
 "A stochastic implementation of the APCI model for mortality projections" (2019) by S. J. Richards, I. D. Currie, T. Kleinow and G. P. Ritchie, British Actuarial Journal, 24, pages 1-26
 "Parameter risk in time-series mortality forecasts" (2016) by T. Kleinow and S. J. Richards, Scandinavian Actuarial Journal, 2016(10), pages 1-25
 "The best available approximation to the truth" (2013) by Richards, S. J., Editorial in British Actuarial Journal, Vol 18, Part II, doi: 10.1017/S1357321713000263
 "A Value-at-risk framework for longevity trend risk" (2012) by Richards, S. J., Ritchie, G. P. and Currie, I. D., Preview: Faculty of Actuaries 2012
 "Assessing longevity risk and annuity pricing with the Lee-Carter model" (2009) by Richards, S. J. and Currie, I. D., Preview: Faculty of Actuaries 2009
 "Detecting year-of-birth mortality patterns with limited data" (2008) by Richards, S. J., Journal of Royal Statistical Society (Series A), 171, Part 1, 1--20
**Only available to licence-holders of our software products.
 "International trends in pensioner longevity" (2007) by Richards, S. J., International News, Society of Actuaries, July 2007
**Only available to licence-holders of our software products.
 "Two-dimensional mortality data: patterns and projections" (2007) by Richards, S. J., Ellam, J. R., Hubbard, J., Lu, J. L. C., Makin, S. J. and Miller, K. A., Presented to Sessional Meeting of Faculty of Actuaries, March 19th 2007
This paper was awarded the Faculty prize for best paper presented to a sessional meeting in the session 2006/2007.
 "The importance of year of birth in two-dimensional mortality patterns" (2005) by Richards, S. J., Kirkby, J. G. and Currie, I. D., British Actuarial Journal, 12, I, 5--61

We just want to experiment with GLMs and survival models. What software should we use without incurring large costs?

Try R, which is free, robust and reliable. If you want to step up to something more sophisticated later, then Longevitas will fit a wider variety of models. If you are worried about back-testing, Longevitas also generates files suitable for reading into R and will also generate R command scripts.

Will Longevitas run on our computers?

If you have a web browser and an Internet connection, you can run Longevitas.

What's the minimum amount of data I need for Longevitas?

Technically the minimum amount of data is one event. In practice, the smallest data set we have seen used was a pension scheme with 6,000 pensioners.

Our portfolio isn't even that big. What can we do?

Try mortalityrating.com, which uses a model of mortality by age, gender and postcode-driven lifestyle to rate small portfolios with little or no experience data. All you need are the following five data items for your pensioners: date of birth, gender, commencement date, annual pension and the full U.K. postcode.

Why would we consider Longevitas?

  1. The latest mortality models at the click of a mouse-button.
  2. Integrated support from a leading industry expert on modelling mortality and other demographic risks.
  3. No software to install!
  4. Use anywhere in the world.
  5. Intuitive, menu-driven approach - no programming language to learn!
  6. Online library of what works, what doesn't work (and why!)
  7. Unique expert system suggests improvements to your models based on fifteen years' experience of modelling mortality.
  8. Automatic report generation to document models.
  9. Automatic rate-table generation for use in pricing and reserving.

Can mortality have a big enough effect to make a difference to profitability?

Yes. Richards and Jones (2004) showed the impact on pension and annuity reserves of five rating factors besides age. Each one of them could cause a change which could wipe out a typical annuity pricing margin.

Standard tables express mortality rates by age and gender, so why can't we just pick one of those?

Standard tables are fine as they go, but they usually only use two rating factors: age and gender. Richards and Jones (2004) found four further rating factors beyond age and gender, all of which were material for pricing and reserving.

Incidentally, Longevitas has a charting tool which enables you to visually modify standard tables to better match the modelled mortality patterns observed in your portfolio. We also have a blog entry questioning the usefulness of standard tables in modelling work.

I don't see how postcodes can be relevant for mortality. Surely pension size is all that is needed?

See our Institute of Actuaries paper, which was peer-reviewed and details how and why postcodes work well for explaining mortality variation. For a generally lighter read without the maths, try our article in Life and Pensions magazine.

How can the same techniques be applied to both longevity and other risks such as persistency or transfer? Aren't they completely different processes?

First, there are some decrements which many of the same underlying features as mortality, such as critical illness. Mortality-orientated models tend to work well here.

Second, transfer and persistency risks do indeed have different behaviour, which is why we have a separate set of variables for application there.

Incidentally, we have a blog entry on the importance of using survival models for competing risks.

What can we do for non-U.K. data where there are no postcodes?

Versions of Longevitas exist for the U.S.A., Canada and the Netherlands, each of which has a hierarchical postcode-like structure, e.g. the nine-digit zip code in the United States. Other countries, such as France and Germany, can use address-based profiling.

I don't see how postcodes can be relevant for mortality. Surely pension size is all that is needed?

See our Institute of Actuaries paper, which was peer-reviewed and details how and why postcodes work well for explaining mortality variation. For a generally lighter read without the maths, try our article in Life and Pensions magazine.