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Graduation is the process whereby smooth mortality rates are created from crude mortality rates. Smoothness is an important part of graduation, but another is the extrapolation of mortality rates to ages at which data may be unreliable or even non-existent.
Correlation complications
A basic result in probability theory is that the variance of the sum of two random variables is not necessarily the same as the sum of their variances.
Discounting longevity trend risk
Establishing the capital requirement for longevity trend risk is a thorny problem for insurers with substantial pension or annuity payments.
Parallel (Va)R
One of our services, the Projections Toolkit, is a collaboration with Heriot-Watt University. Implementing stochastic projections can be a tricky business, so it is good to have the right people on the job.
Groups v. individuals
We have previously shown how survival models based around the force of mortality, μx, have the ability to use more of your data. We have also seen that attempting to use fractional years of exposure in a qx model can lead to potential mistakes. However, the Poisson distribution also uses μx, so why don't we use a Poisson model for the grouped count of deaths in each cell?
Following the thread
Gavin recently explored the topic of threads and parallel processing. But what does this mean from a business perspective?
Competitive eating
I've previously suggested parallel processing might have a touch of the infernal about it, and further evidence might be how it allows us to usefully indulge in one of the seven deadly sins, that of gluttony.
Longevity and the 2011 Census
The Continuous Mortality Investigation (CMI) has just announced its decision to postpone the release of its mortality projection model until 2013, the main reason being to properly allow for the impact of the 2011 Census.
Extracting the (data) value
Risk management is about properly understanding your risk factors and managing accordingly. In a modern actuarial context, this is about a lot more than a simple comparison against a standard table.
Canonical correlation
At our seminar earlier this year I looked at the validity of assumptions underpinning some stochastic projection models for mortality. I looked at the assumption of parameter independence in forecasting, and examined whether this assumption was borne out by the data. It transpires that the assumption of independence is a workable assumption for some models, but not for others. This has important consequences in a Solvency II context — an internal model must be shown to have assumptions grounded in fact.