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We have written in the past about some of the reasons why we don't use Excel to fit our models. However, we do use Excel for validation purposes — fitting models using two entirely separate tools is a good way of checking production code. That said, there are some important limits to Excel, especially when it comes to fitting projection models.
Wind-up and buy-out - the cheaper option?
The words "cheap" or "cheaper" are not normally seen in the same sentence as pension scheme wind-up or buy-out. However, my challenge is whether it is not indeed the cheaper option after taking into account the capitalised costs of running a pension scheme for another 10 or 20 years.
(Un)Fit for purpose
Academics lay great store by anonymous peer review and in openly publishing their results. There are good reasons for this — anonymous peer review allows expert third parties (usually two) to challenge assumptions without fear of retribution, while open publishing allows others to test things and find their limitations.
Demography's dark matter: measuring cohort effects
My last blog generated quite a bit of interest so I thought I'd write again on cohorts. It's easy to (a) demonstrate the existence of a cohort effect and to (b) fit models with cohort terms, but not so easy to (c) interpret or forecast the fitted cohort coefficients. In this blog I'll fit the following three models:
Forecasting with cohorts for a mature closed portfolio
At a previous seminar I discussed forecasting with the age-period-cohort (APC) model:
$$ \log \mu_{i,j} = \alpha_i + \kappa_j + \gamma_{j-i}$$
A second pension-scheme revolution
In his book Unseen Revolution, Peter Drucker drew attention to the structural changes in economic ownership which were silently ushered in with the growth of corporate pension schemes.
Spotting quality issues with limited data
In an earlier posting I showed how to use the Kaplan-Meier function to identify subtle data problems. However, what can you do when you don't have the detailed information to build a full survival curve?
Effective dimension
Actuaries often need to smooth mortality rates. Gompertz (1825) smoothed mortality rates by age and his famous law was a landmark in this area. Figure 1 shows the Gompertz model fitted to CMI assured lives data for ages 20–90 in the year 2002. The Gompertz Law usually breaks down below about age 40 and a more general smooth curve would be appropriate. However, a more general smooth curve would obviously require more parameters than the two for the simple Gompertz model.
Boundless confidence?
We've talked repeatedly about a key advantage of statistical models over deterministic ones — specifically, that they provide confidence intervals in addition to a best estimate.
S2 mortality tables
The CMI has released the long-awaited S2 series of mortality tables based on pension-scheme data. These are the first new tables since the CMI changed its status (the S2 series is only available to paying subscribers, unlike prior CMI tables).