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Posts feedConditional tail expectations
In a recent posting I looked at the calculation of percentiles and quantiles, which underpin many calculations for ICA and Solvency II. Simply put, an \(\alpha\)-quantile is the value which is not expected to be exceeded \(\alpha\times 100\)% of the time. This value is denoted \(Q_{\alpha}\). Mathematically, for a continuous random variable, \(X\), and a given probability level \(\alpha\) we have:
$$\Pr(X\leq Q_\alpha)=\alpha$$
Don't cut corners
An important class of mortality-projection models is the Cairns-Blake-Dowd (CBD) family.
Quantiles and percentiles
Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. They are generally described as q-quantiles, where q specifies the number of intervals which are separated by q−1 points.
Creative thinking around longevity risk
The U.K. has been a hotbed of innovation when dealing with the longevity risk found in pension schemes.
Excel's limits
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.